## Function Composition Questions and Answers

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Let f(x) = x^2, \; g(x) = x - 3. Find (f \circ g)(x).

Let f(x) = 3x + 2 and g(x) = - x + 2. Find f(f(-x))

For f(x) = sqrt(x) and g(x) = x + 7, find the following functions. a. (fog)(x) b. (gof)(x) c. (fog)(2) d. (gof)(2)

Let f(x) = 1/2x + 8 and h(x) = 8x + 8. Find h(f(x)).

Suppose that the functions q and r are defined as follows. q(x) = x^2 + 6; r(x) = sqrt(x + 9). Find the following. A) (qor)(7) B) (roq)(7)

Given f(x) = 2(x+1)^3 and g(x) = x^2, find each of the following. a. (f o g)(-3) b. (g o f)(x)

Consider the following functions: f(x) = x^2 + 4, \; g(x) = x^2 - 3. Find (g \circ f)(x).

Consider the following functions: f(x) = x^2 + 4, \; g(x) = x^2 - 3. Find (f \circ g)(x).

Consider the following functions: f(x) = x + 5, \; g(x) = 2x + 4. Find (g \circ f)(1).

Consider the following functions: f(x) = \sqrt{x}, \; g(x) = x - 2. Find (f \circ g)(3).

Consider the following functions: f(x) = \sqrt{x}, \; g(x) = x - 2. Find (g \circ f)(x).

Consider the following functions: f(x) = \sqrt{x}, \; g(x) = x - 2. Find (f \circ g)(x).

Consider the following functions: f(x) = x + 5, \; g(x) = 2x + 4. Find (g \circ f)(x).

Consider the following functions: f(x) = x + 5, \; g(x) = 2x + 4. Find (f \circ g)(x).

Consider the following functions: f(x) = x^2 + 4, \; g(x) = x^2 - 3. Find (f \circ g)(4).

Consider the following functions: f(x) = x^2 - 6x, \; g(x) = x + 2. Find (f \circ f)(x).

Consider the following functions: f(x) = x^2 + 4, \; g(x) = x^2 - 3. Find (g \circ f)(4).

Consider the following functions: f(x) = x + 5, \; g(x) = 2x + 4. Find (f \circ g)(1).

Consider the following functions: f(x) = \sqrt{x}, \; g(x) = x - 2. Find (g \circ f)(3).

Consider the following functions: f(x) = x^2 - 6x, \; g(x) = x + 2. Find (g \circ f)(x).

Consider the following functions: f(x) = x^2 - 6x, \; g(x) = x + 2. Find (f \circ g)(x).

If f(x)=-x+1, evaluate f(x+h).

Let f (x) = x^2 + x and g (x) = 5 x^2 - 1. a. Find the function (f . g) (x). b. Find the domain.

Let f(x) = x^2 - x + 4 and g(x) = 2x + 5. Find g(2) and f(g(2)).

(a) Determine fog, gof , and the domain of fog. (b) Use a graphing utility to graph fog and gof. Determine whether fog=gof.

find fog, gof , and the domain of fog. (b) Use a graphing utility to graph fog and gof. Check whether fog=gof.

Let f (x) = x^2 + 2 and h (x) = x + 4. Find the value of the following composite function. (f of h)(-2)

Given f(x) = 3x and g(x) = 1 + x^2. Find (f o g)(5) and (g o f)(5).

Suppose h (x) = 10 square root -3 x^2 - 9 x + 5, where h (x) = (f of g) (x). If f (x) = 10 square root x, what is g (x)? A) g (x) = square root -3 x^2 - 10 x + 5. B) g (x) = square root -3 x^2 - 9...

If f(x) = x^4 + 8, g(x) = x - 1, h(x) = sqrt x, then f o g o h(x) = ________.

Given functions f(x) = 18x^2 + 3 and g(x) = -5/x, answer the following questions. a. (fog)(-3) b. (fof)(1) c. (gof)(x) d. (gog)(x)

Let f(x) = x^2 and g(x) = \dfrac{1}{x} - 2x. Find f(g(x)) and g(f(x)).

Find the domain of f (g (x)), if: f (x) = 1 / x g (x) = 1 / (x + 4)

True or false? If g is continuous at 3 then the composite function (g \circ g)(x) = g(g(x)) is continuous at 3.

Let f(x) = 1/(x^2 - 3) and g(x) = x^2 + 2. Evaluate and simplify (fog)(x).

For the following pair of functions, form the composition f of g. f(x) = 3x - 1 g(x) = x^2 - 2x + 1

Consider the following functions: f(x) = 2x^2 - 9x + 2, \; g(x) = 1 - 6x, \; h(x) = x^2 - 4. Determine (h -g)(-7).

Consider the following functions: f(x) = 2x^2 - 9x + 2, \; g(x) = 1 - 6x, \; h(x) = x^2 - 4. Find (f \cdot h)(x).

Consider the following functions: f(x) = 2x^2 - 9x + 2, \; g(x) = 1 - 6x, \; h(x) = x^2 - 4. Find (f \circ g)(x).

Given functions f and g, find: (a) (f circ g) (x) and its domain. (b) (g circ f) (x) and its domain. f(x) = sqrt x, g(x) = x + 3

Given the following functions below. f(x) = x^2, g(x) = x + 7 Find (g o f)(x).

Given the following functions below. f(x) = x^2, g(x) = x + 7 Find (g o g)(x).

Given the following functions. f(x) = 5 - x, g(x) = x^2 - 3x Find the domain of (f - g)(x).

Given the following functions. f(x) = 5 - x, g(x) = x^2 - 3x

Given the following functions. f(x) = 5 - x, g(x) = x^2 - 3x Find the domain of (f + g)(x).

Given the following functions below. f(x) = x^2, g(x) = x + 7 Find (f o f)(x).

Given the following functions below. f(x) = x^2, g(x) = x + 7 Find the domain of (g o g)(x).

Given the following functions below. f(x) = x^2, g(x) = x + 7 Find the domain of (f o f)(x).

Given the following functions below. f(x) = x^2, g(x) = x + 7 Find the domain of (f o g)(x).

Given the following functions below. f(x) = x^2, g(x) = x + 7 Find the domain of (g o f)(x).

Let f(x) = 3x + 2 and g(x) = 2x^2 + 3x. Find (f o g)(x).

Consider f (x) = square root x^2 + 2 and g (x) = x^2 + 8. Find: a. f of g. b. g of f.

If f (x) = 2 x^2 and r (x) = square root 7 x, find a simplified formula for f(r(x)).

Consider f (x) = 7 x + 7 and g(x) = x^3. Find f of g.

(a) Evaluate fog, gof , and the domain of fog. (b) Use a graphing utility to graph fog and gof. Determine whether fog=gof.

Find the functions (a) f o g, (b) g o f, (c) f o f, and (d) g o g and their domains.

(a) find out fog, gof , and the domain of fog. (b) Use a graphing utility to graph fog and gof. Determine whether fog=gof.

(a) find fog, gof , and the domain of fog. (b) Use a graphing utility to graph fog and gof. Determine whether fog=gof.

Given the two functions f (x) =x^2 - 4 x + 1 and g (t) = 1 - t. a. Find and simplify f (g (t)). b. Find and simplify g (f(x)).

Write the function in the form y = f(u) and u = g(x). Then find \dfrac{dy}{dx} as a function of x. y = e^{3 - 5x} Choose the correct form of y in terms of u. A. y = e^{-3 + 5u}, where u = -x B....

Given the functions f(x) = x + 2 and g(x) = 3x - 1, find f of g(x) and f of g(3).

Let f(u) = \sqrt3{u} and g(x) = u = 2 + 9x^2. Find (f \circ g)'(1).

Use f(x) = 5x - 4 and g(x) = 3 - x^2 to evaluate the expression. A) f(f(2)) B) g(g(3))

Use the table below to evaluate the following: (g \circ g)(1). | x | -2 | -1 | 0 | 1 | 2 | f(x) | -1 | 2 | -2 | 1 | 0 | g(x) | 1 | -1 | 0 | 0 | -2

Given that f(x) = -x^2 + 5x, determine (f \circ f)(x).

Use the table below to evaluate the following: (f \circ f)(0). | x | -2 | -1 | 0 | 1 | 2 | f(x) | -1 | 2 | -2 | 1 | 0 | g(x) | 1 | -1 | 0 | 0 | -2

Use the table below to evaluate the following: (f \circ g)(-1). | x | -2 | -1 | 0 | 1 | 2 | f(x) | -1 | 2 | -2 | 1 | 0 | g(x) | 1 | -1 | 0 | 0 | -2

Consider the following functions: f(x) = -x^2 + 5x, \; g(x) = 2x - 6. Determine (f \circ g)(x).

If f(x) = 1 - 3x, \enspace g(x) = \cos x, find the functions: (a) f \circ g (b) g \circ f (c) g \circ g (d) f \circ f

Given the function f(x) = 1/3x - 2 and the function g(x) = 5x^2 + 2x + 6. Give your answer as an integer or a simplified fraction. Evaluate f(g(5)).

If f (x) = 2 x - 1 and g (x) = 3 x + 5, what is f(g (5))?

Given that f(x) = 2x - 6, determine (f \circ f)(x).

Consider the following functions: f(x) = -x^2 + 5x, \; g(x) = 2x - 6. Determine (g \circ f)(x).

Consider the following functions: p(x) = x^2 + 6, \; q(x) = \sqrt{x + 1}. Find (q \circ p)(3).

Consider the following functions: p(x) = x^2 + 6, \; q(x) = \sqrt{x + 1}. Find (p \circ q)(3).

Consider the following functions: f(x) = \dfrac{3}{4}x - 3, \; g(x) = 9x^2 + 6x + 7. Find f(g(2)).

Consider the following functions: f(x) = \dfrac{3}{4}x - 3, \; g(x) = 9x^2 + 6x + 7. Find g(f(8)).

Given that f(x) = 6x + 5 and g(x) = -3, calculate: (a) f(g(3)) (b) g(f(2))

Find the composite functions (f \circ g) and (g \circ f). What is the domain of each composite function? (Simplify your answers completely. Enter your domains in interval notation.) f(x) = x^6 \\ g...

Let a(x) = x^2 - 5x, b(x) = line x + 2 line, c(x) = - square root 3x, d(x) = 2/x. Find (b o d)(x).

Let f (x) = - 4x - 1 and g (x) = x^2 + 2. Find (f of g) (-2).

If f(x) = x^2 + 2x - 8 and g(x) = 2x - 5, find g \circ f.

If f(x) = \cos x, \enspace g(y) = \frac{\pi}{6}y^2 + y - 1, \enspace h(z) = \sqrt{1 + z + z^2}, then find (f \circ g \circ h)'(0).

f(x) = \dfrac{1 - x}{1 + x} and g(x) = \dfrac{1 + x}{1 - x} Find: (f \circ g)(x) \\ (f \circ f)(x) \\ (g \circ f)(x) \\ (g \circ g)(x)

If f(x) = x^2 and g(x) = x - 3, find the composite functions f \circ g and g \circ f.

Consider the following functions: f(x) = x - 7, \; g(x) = 6x^2. Determine (f - g)(x) and state its domain.

Let f(x) = x^3 + 7, g(x) = x^2 - 2, and h(x) = 4x + 4. Find the rule for the function fgh.

Find (g o f)(3) if f(x) = -4x + 2 and g(x) = x^2 + 1.

Let f(x)=4x+9 and g(x)=x^2-1, find f(g(7)).

Given the following: f(x) = 10x + 10 and g(x) = 30 - 16x, find (f + g)(x).

If f(x) = 4x - 2 and g(x) = x^2 - 2x - 3, find (fog) and (gof)(1).

Solve for j. 5j^3 + 23j - 10 = 0

Given f(x) = \dfrac{1}{x - 3} and g(x) = \sqrt{x + 5}. (a) Determine (f \circ g)(x). (b) Determine (f \circ g)(11). (c) Determine the domain of (f \circ g)(x) in interval notation.

Find the rules for the composite functions f \circ g and g \circ f. f(x) = 3\sqrt{x} + 6; \quad g(x) = x^2 + 7

For f (x) = x^2 +6 and g(x) = x^2 - 6, find the following functions. a. (f of g) (x). b. (g of f) (x). c. (f of g) (4). d. (g of f) (4).

Given f(x) = square root x + 24 and g(x) = x^2 - 17, find (f o g) (3).

Given f (x) = square root x + 24 and g (x) = x^2 - 17, find: a. g of f. b. (f of g) (3).

Let f(x) = 2x^2 - 5 and g(x) = sqrt(3x - 4). Find (fog)(x) and state the domain of the function.

Given f(x) = square root x + 24 and g(x) = x^2 - 17, find g o f.

Let the variable x represents Mabel's age. Write the following in terms of x. "40 less than twice Mabel's age"

Evaluate (g o f)(-1) using the graphs of y = f(x) and y = g(x) shown below.

Evaluate (f o g)(4) using the graphs of y = f(x) and y = g(x) shown below.

Evaluate (g o f)(0) using the graphs of y = f(x) and y = g(x) shown below.

Evaluate (f o g)(-1) using the graphs of y = f(x) and y = g(x) shown below.

Let f(x) = \dfrac{x - 3}{x + 5} and g(x) = 1 + \dfrac{3}{x}. Find and simplify as much as possible f \circ g(x).

For the following function and its properties, sketch a graph. g(x) where g(2) = 0,\enspace \lim_{x \to 4}g(x) = 2,\enspace g(4) = 5.

Prove that the function h(x)=(1-x^2)^1/3 is its own inverse by showing that h(h(x)) =x.

If f(x) = x^2 - 8 and h(x) = 2x + 4, h(f(x)) = __________.

Determine exact value of the each function for the given angle.

Consider the following equations: f(x) = 2x^2 - 3x + 1, \; g(x) = x + 5, \; h(x) = 2\sqrt{x-3}. Find f(g(x)).

Consider the following equations: f(x) = 2x^2 - 3x + 1, \; g(x) = x + 5, \; h(x) = 2\sqrt{x-3}. Find g(f(-2)).

Find (a) f + g, (b) f - g, (c) fg, and (d) f/g and state their domains.

If f(x) = ln x and g(x) = x2 - 9, find the functions (a) f o g, (b) g o f, (c) f o f, (d) g o g, and their domains.

Find the functions (a) f \circ g, (b) g \circ f, (c) f \circ f, and (d) g \circ g and their domain. f(x) = \sqrt{x}, \enspace g(x) = \sqrt[3]{1 - x}

Find a formula for f(g(x)) if g(x) = 8x and f(x) = 4x^2 - 7. Then find f(g(2)).

Let f(x) = \sqrt{x} and g(x) = -\frac{1}{x^2}. Find the formulas for all four compositions (f(f(x)), g(g(x), f(g(x)), g(f(x))) and write their domains.

If f(x) = x + \frac{1}{x} and g(x) = x^2, give a simplified formula for each of the composite functions: (a) f(g(x)) (b) g(f(x)) (c) f(f(x))

Use the graphs to evaluate each of the three (3) expressions below. 1. f(g(3)) 2. f(f(5)) 3. g(g(2))

Given the graph of f below, find (fcirc f)(-2). A. 1 B. 2 C. 4 D. -2 E. 5

Given that f(x) = 2x+8,g(x) = frac{5x-2}{4},h(x) = frac{2x+6}{x} Find: i) f(-5) ii) g(f(0)) iii) f(h(3)) iv) (h circ f)(x) v) h^{-1}(x)

Suppose the demand for a certain brand of a product is given by D(p) =-p^2/448 + 150, where p is the price in dollars. If the price, in terms of the cost c, is expressed as p(c) =4c-28, find the de...

Let f(x) = 3x^2 + 7 and g(x) = x - 3. (a) Find the composite function (fog)(x) and simplify. (b) Find (fog)(-2).

Determine whether the statement is true or false. If it is true, explain why. If it is false, explain why or give an example that disproves the statement. If f and g are functions, then f \circ g...

Find g(x) given that: f(g(x)) = \ln \left ( x^2 + 4 \right ) f(x) = \ln (x^2), g(x) is greater than 0, \forall x

Let g(x) = x - 1 / x, find the y = f(x) so that (f o g)(x) = x / x + 1. A) x +2 B) 1 / 2 + x C) 2 - x D) 2 + x / 2 - x E) 1 / 2 - x

Let g(x) = x + 1 and h(x) = (fog)(x) = x^2 + 2x + 1. Find f(x) and (gof)(x).

Given f(x) = x^2, g(x) = sqrt(x), h(x) = 2x, find fohog(16).

Express the function in the form f \circ g. u(t) = \frac{\csc (t)}{5 + \csc(t)} \left\{ f(t), g(t) \right\} =

Find f \circ g \circ h. f(x) = \tan (x), g(x) = \frac{x}{x - 4}, h(x) = \sqrt[3]{x}

Find f \circ g \circ h. f(x) = x + 5, g(x) = 4x, h(x) = x - 5

Express the function in the form f \circ g. G(x) = \sqrt[3]{\frac{x}{9 + x}} \left\{ f(x), g(x) \right\} =

Let y = 3^u, u = v^2, v = tan x, then y = f(x) = _____.

If f(x) = 1/(x - 1), then f(f(x)) = _____.

Use the values for the functions f and g given in the table below to compute f(g(2)). x 0 1 2 3 4 5 6 f(x) -10 5 0 4 9 -2 1 g(x) -1 0 4 2 5 -1 0 a) 9 b) 4 c) 0 d) -1e) 5

Consider the following function: g(x) = 2x + 8. Find (g \circ g) (x).

Consider the following function: g(x) = 2x + 8. Find the domain of (g \circ g) (x).

Consider the following function: f(x) = \dfrac{2}{x}. Find the domain of (f \circ f) (x).

Consider the following function: f(x) = \dfrac{2}{x}. Find (f \circ f) (x).

Consider the following functions: f(x) = \dfrac{2}{x}, \; g(x) = 2x + 8. Find (g \circ f) (x).

Consider the following functions: f(x) = \dfrac{2}{x}, \; g(x) = 2x + 8. Find the domain of (g \circ f) (x).

Consider the following functions: f(x) = \dfrac{2}{x}, \; g(x) = 2x + 8. Find the domain of (f \circ g) (x).

Consider the following functions: f(x) = \dfrac{2}{x}, \; g(x) = 2x + 8. Find (f \circ g) (x).

Find and simplify as much as possible fog(x). f(x) =(x - 3)/(x + 5) and g(x) = 1+3/x

If f (x) = square root x and g (x) = x^3 + 8, simplify the expressions (f of g)(2), (f of f)(36), (g of f)(x), and (f of g)(x).

Find f of g of h. f(x) = x - 4, g(x) = sqrt x, h(x) = x - 4

At a certain factory, the total cost of manufacturing q units is C(q) =0.3q^2 + q + 900 dollars. It has been determined that approximately g(t) = t^2 + 100t units are manufactured during the first...

Let f(x) = x^2 - 4x + 5 and g(x) = 3x + 5. (a) Find the composite function (fog)(x) and simplify the results. (b) Find the composite function (gof)(x) and simplify the results. (c) Find (fog)(-2).

Let f(x) = sqrt(x), g(x) = x - 2, and h(x) = x. Find and simplify each expression. a) (fog)(171) b) (foh)(9)

Differentiate the following. y = 3x^2 tan^(-1)(2x).

If f0(x) = x2 and fn+1(x) = f0(fn(x)) for n = 0, 1, 2,..., find a formula for fn(x).

Let f(x) = 3x+2 and g(x) = 2/(x-1). Find f(g(0)) + 4.

Let f(x) = x / x - 2, find the g(x), so that (fog)(x) = x.

If g(x) = cos 2x, find g(x - pi over 2).

Find the derivative of the function. f(x) = csc (sin^2 (x))

Use the given graphs of f and g to evaluate each expression, or explain why it is undefined. (a) f(g(2)) (b) g(f(0)) (c) (f [{MathJax fullWidth='false' \circ }] g) (0) (d) (g [{MathJax fullWidth='f...

Use the table to evaluate each expression. (a) f(g(1)) (b) g(f(1)) (c) f(f(1)) (d) g(g(1)) e)gof(3)

Find the functions and their domains. f(x) = 2x + 5, g(x) = x^2 + x. (a) fog (b) gof (c) fof (d) gog

Consider the following functions: f(x) = x - 7, \; g(x) = \sqrt{x}, \; h(x) = x - 7. Find f \circ g \circ h.

Express the function in the form f(g(h)). H(x) = sec^4(sqrt(x))

Express the function in the form f(g(h)).R(x) = sqrt(sqrt(x)-1)

Find fogoh.f(x)=|x-4|

Express the function in the form f(g). u t() = tan t/(1+tan t)

Express the function in the form f(g). G(x) = cube root(x/(1 + x))

Express the function in the form f(g). F(x) = cuberoot(x)/(1+cuberoot(x))

Let f (x) = sin x and h (x) = 2x. Find the value of (f of h) (pi / 6).

Find f o g o h. f(x) = 3x - 2, g(x) = sin x, h(x) = x2

Express the function in the form f o g. F(x) = (2x + x2)4

Express the function in the form f(g). F(x) = cos^2 x

Find f(g(h)). f(x) = tanx, g(x) = x/(x-1), h(x) = cuberoot (x)

Find f (g(h)). f(x) = sqrt(x - 3), g(x) = x^2, h(x) = x^3 + 3

Let f(x) = x^2 and g(x) = 1/x - 2x, find g(f(x)).

Find the functions (a) fog (b) gof (c) fof (d) gog and their domains. and their domains. f(x) = 1 - 3x, g(x) = cos x

Find the functions (a) fog (b) gof (c) fof (d) gog and their domains. and their domains. f(x) = x - 2, g(x) = x2 + 3x +4

Find the functions (a) fog (b) gof (c) fof (d) gogand their domains. f(x) = x2 - 1, g(x) = 2x + 1

Let f(x) = e^(x^2 + 5x + 6) and g(x) = 1/x^2. Find (gof)(x), express the answer as an exponential function.

Given f(x) = x^3 + 3 and g(x) = 3rd root of {x^4 + 5}, find (f of g)''(2).

If f(x) = x^6 and g(x) = 4x + 5, find f(g(x)).

Find the first derivative of the following: y = (1 + cos^2 x)^6.

Find the domain of each function. g(t) = \sin (e^- t)

Determine (f of g)(x) and (g of f)(x) given f(x) = 4x + 2 and g(x) = sqrt{x - 8}.

If f(x) = \sqrt{x} and g(x) = x^3 + 17, simplify the following expressions. (f \circ g)(2) (f \circ f)(36) (g \circ f) (x) (f \circ g) (x)

Meteorology The normal daily high temperature T (in degrees Fahrenheit) in Savannah, Georgia can be approximated by where t is the time (in months), with t = 1 corresponding to January. Find the no...

Evaluate f(1)g(1) from the graph.

Evaluate f(g(1)) from the graph.

Evaluate g(f(-1)) from the graph.

For which of the following pairs of functions is equal to f(g(x))? (a) (b) (c)

For the given function. f(x)= square root of{2x}, g(x) = 5x-8 Find (f cdot g)(x).

Find f(g( - 4)) and g(f(-4)) for f(x) = 5x - 1 and g(x) = x^2 + 4.

The number of bacteria in a refrigerated food product is given by where T is the temperature of the food in degrees Celsius. When the food is removed from the refrigerator, the temperature of the f...

The spread of a contaminant is increasing in a circular pattern on the surface of a lake. The radius of the contaminant can be modeled by , where r is the radius in meters and t is time in hours si...

Three siblings are three different ages. The oldest is twice the age of the middle sibling, and the middle sibling is six years older than one-half the age of the youngest. (a) Write a composite fu...

Decomposing a Composite Function In Exercise, find two functions f and g such that (f [{MathJax fullWidth='false' \circ }] g)(x) = h(x). (There are many correct answers.) h(x) = (1 - x)3

Find two functions f and g such that (f og)(x) = h(x). (There are many correct answers.)

Determine two functions f and g such that (fog)(x) = h(x). (There are many correct answers.)

Find two functions f and g such that (f g)(x) = h(x). (There are many correct answers.)

Find f(g(-3)) and g(f(-3)), f(x) = 2x - 1 g(x) = x^2 + 4

Use the functions f(x) = 1/8 x - 3 and g(x) = x^3 to find the indicated value or function. (f^(-1) o g^(-1))(1).

Find two functions f and g such that (fog)(x) = h(x). h(x) = (2x + 1)^2.

Find (a) fog, (b) gof, and (c) fog(0) if possible. f(x) = x^3, g(x) = 1/x.

Determine the domains of (a) f, (b) g, and (c) fog. Use a graphing utility to verify your results. f(x) = 2/absolute of x, g(x) = x - 1.

Function f, g, and h are given by f(x) = 12 - sqrt(x), g(x) = 4/x^2 and h(x) = 8x - 4. A) Calculate (foh)(5). B) Calculate (fogoh). C) Find the inverse of f(x).

Consider the function f and g defined by the equation f(x)=3x+2 and g(x)= 1/3(x-2). Show that g circ f=1.

Consider the function f and g defined by the equation f(x)=3x+2 and g(x)= 1/3(x-2). Show that f circ g=1.

For the given function f and g, find the indicated composition. f(x) = -4x + 8, g(x) = 3x + 2. Find (gof)(x).

Find two functions f and g such that . (There are many correct answers.) h(x) = (x + 4)2 + 2(x + 4)

Suppose f(x) = sqrt(x) and g(x) = cube root of (1 - x). Find fog, gof, and fof.

Find two functions f and g such that (f \circ g)(x) = h(x). (There are many correct answers.) h(x) = (x + 3)^{3/2} + 4(x + 3)^{1/2}

Find two functions f and g such that (f \circ g)(x) = h(x). (There are many correct answers.) h(x) = \sqrt[3]{x^2 - 4}

Use the function tables for f (x ) and g(x) to evaluate each expression: x f(x) 1 2 3 6 4 5 6 7 x g(x) 2 4 3 2 5 6 7 0 a) (f+g)(3) = _____ b) (fg)(3) = _____ c) (f circ g)(2) = __...

Use f (x) = x + 4 and g(x) = 2x - 5 to find the specified function. (gof)-1.

Use the functions f (x) = x + 4 and g(x) = 2x - 5 to find the specified function. (f o g)-1

If f(x) = ax + b and g(x) = cx + d , then when is (f\circ g)(x) = (g \circ f)(x) ?

Given f(x) = 3x + 5 and g(x) = 5 - x, find: a) f circle g b) g circle f c) (f circle g)(0)

(a) Determine fog, gof , and the domain of fog. (b) Use a graphing utility to graph fog and gof. Determine whether fog=gof.. f (x) = x2/3, g(x) = x6

Determine the domains of (a) f, (b) g, and (c)fog . Use a graphing utility to verify your results.

Given f(x) = (1/8)x - 3 and g(x) = x^3 to find (g^-1 circle f^-1).

Given f(x) = (1/8)x - 3 and g(x) = x^3, find (g^-1 circle g^-1)(-4)

Given f(x) = (1/8)x - 3 and g(x) = x^3, find (f^-1 circle f^-1) (6)

Finding the Domain of a Composite Function, determine the domains of (a) f, (b) g, and (c) fog. Use a graphing utility to verify your results.

Determine (a) (f + g)(x), (b) (f - g)(x), (c) (fg)(x), and (d) (f/g)(x). What is the domain of f/g?

For the functions f(x)=x^2, g(x)=1-x, find (a) (f+g)(x) (b) (f-g)(x) (c) (fg)(x) (d) (f/g)(x). What is the domain of f/g?

For the functions f(x)=cubed root (x-1) g(x)=x^3+1 find (a) f composed with g (b) g composed with f (c) (If possible) (f composed with g)(0)

For the functions f(x)=x^2, g(x)=x-1 (a) f composed with g (b) g composed with f (c) (If possible) (f composed with g)(0)

The sales S (in thousands of units) of a cleaning solution after x hundred dollars is spent on advertising are given by S = 10(1 - ekx). When $500 is spent on advertising, 2,500 units are sold. (a...

For the functions f(x)=1/x and g(x)=x+3 determine the domains of (a) f (b) g (c) f dot g

For the functions f(x)=x^(1/4) and g(x)=x^4, determine the domains of (a) f (b) g (c) f dot g

A square concrete foundation is a base for a cylindrical tank (see figure). (a) Write the radius r of the tank as a function of the length x of the sides of the square. (b) Write the area A of the...

A pebble is dropped into a calm pond, causing ripples in the form of concentric circles. The radius r (in feet) of the outer ripple is r(t) = 0.61, where t is the time in seconds after the pebble s...

Use the graphs of y = f(x) and y = g(x) to evaluate the function. (g^(-1) circ f)(3)

Use the graphs of y = f(x) and y = g(x) to evaluate the function. g( f (-4))

Use the graphs of y = f(x) and y = g(x) to evaluate the function. (f circ g)(2)

Use the graphs of f and g to evaluate the functions. (a) (f comp g)(3) (b) (g comp f)(3)

Use the graphs of f and g to evaluate the functions. (a) (f circ g)(2) (b) (g circ f)(2)

Let f (x) = 14x - 3 and g(x) = 8x^2. Find the indicated value. (g \circ f) (0)

Let f (x) = 14x - 3 and g(x) = 8x^2. Find the indicated value. (f \circ g) (-1)

Let f (x) = 14x - 3 and g(x) = 8x^2. Find the indicated value. (f+g) (-4)

Evaluate the indicated function for f(x) = x^2 - 1 and g(x) = x - 2 algebraically. If possible, use a graphing utility to verify your answer. (f+g)(3)

Find the indicated function for f(x) = x^2 - 1 and g(x) = x - 2 algebraically. If possible, use a graphing utility to verify your answer.(f-g)(0)

Evaluate the indicated function for f(x) = x^2 - 1 and g(x) = x - 2 algebraically. If possible, use a graphing utility to verify your answer. (f-g)(-2)

Evaluate the indicated function for f(x) = x^2 - 1 and g(x) = x - 2 algebraically. If possible, use a graphing utility to verify your answer. (fg)(6)

Evaluate the indicated function for f(x) = x^2 - 1 and g(x) = x - 2 algebraically. If possible, use a graphing utility to verify your answer. (f+g)(1)

A table of values for f, g, f', and g' is given. f(x) g(x) f'(x) g'(x) 1 3 2 4 6 2 1 8 5 7 3 7 2 7 9 If H(X) = g(f(x)), find H (2).

Find (a) f comp g and (b) g comp f. f(x) = cube root(x+5), g(x) = x^3-5

Evaluate the function at the indicated value of x. Round the result to three decimal places. Function: 5^x Value: x = -pi

Find (a) f o g and (b) g o f. f(x) = 2x - 1, g(x) = x^2 + 3

Use a calculator to evaluate the function at the indicated value of x. Round the result to four decimal places. f(x) = 1.45^x, x = 2 pi

Find (a) f o g and (b) g o f. f(x) = x^3-1, g(x)= cuberoot(x+1}.

Find (a) f o g and (b) g o f. f (x) = 5x + 8, g(x) = 2x^2 - 1

Evaluate the indicated function for f(x) = -x^2 + 3x - 10 and g(x) = 4x + 1. (gof)(-2).

Determine whether each x-value is a solution (or an approximate solution) of the equation. 4^{2x - 7} = 64 (a) x = 5 (b) x = 2

Find two functions f and g such that (fog)(x) = h(x). (There are many correct answers.) h(x) = 6/(3x + 1)^3.

Find two functions f and g such that (fog)(x) = h(x). (There are many correct answers.) h(x) = sqrt(4x + 2).

Let f(x) = 3 - 2x, g(x) = sqrt(x), and h(x) = 3x^2 + 2. Find the indicated values. (goh)(6).

Let f(x) = 3 - 2x, g(x) = sqrt(x), and h(x) = 3x^2 + 2. Find the indicated values. (gof)(-3).

Let f(x) = 3 - 2x, g(x) = sqrt(x), and h(x) = 3x^2 + 2. Find the indicated values. (hog)(5).

Find two functions f and g such that (fog)(x) = h(x). (There are many correct answers.) h(x) = (1 - 2x)^3.

Find two functions f and g such that (fog)(x) = h(x). (There are many correct answers.) h(x) = 4/(x + 2).

Find two functions f and g such that (fog)(x) = h(x). (There are many correct answers.) h(x) = cube root of (x + 2)^2.

Let f(x) = 3 - 2x, g(x) = sqrt(x), and h(x) = 3x^2 + 2. Find the indicated values. (f + h)(5).

Let f(x) = 3 - 2x, g(x) = sqrt(x), and h(x) = 3x^2 + 2. Find the indicated values. (f + g)(25).

Find two functions f and g such that (fog)(x) = h(x). (There are many correct answers.) h(x) = (x + 3)^2.

Given (fg)(x)=f(x^2+1) what is g(x)?

Let f (x) = 3 - 2x, g(x)= \sqrt x, and h(x) = 3x^2 + 2, and find the indicated values. (f\circ h)(-4)

Use a calculator to evaluate the function f(x) = ln x at the indicated value of x. Round your result to three decimal places, if necessary. x = 0.46

Use a calculator to evaluate the function f(x) = ln x at the indicated value of x. Round your result to three decimal places, if necessary. x = 21.5

Use a calculator to evaluate the function f (x) = ln x at the indicated value of x. Round your result to three decimal places, if necessary. x = 5/6

Find the exact value of the expression, if possible, without using a calculator. \tan \left[\arcsin \left (-\frac{1}{2} \right) \right]

To find g(x + 1), what do you substitute for x in the function g(x) = 3x - 2?

If f(x, y) = x^2 + y^2, find f_x(0, 8).

Evaluating a Function In Exercise, evaluate the function at each specified value of the independent variable and simplify. (a) f (3) (b) f (12) (c) f (6)

Given the functions f(x) = \sqrt{x} and g(x) = \dfrac{x-5}{2x + 1} \\ A. Find the domain and range of g. B. Solve the equation g(x) = 0 C. Find the domain range of fg.

Evaluating a Composition of Functions, find the exact value of the expression. sec( arctan(-3/5))

Write the function as a composition of two functions. y = (2x+ 9)^7 For f (g(x)) , g(x) =

Find f(g(x)) and g(f(x)) for the given functions. f(x) = 8x 1 , g(x) = 9 3x (Simplify your answer.)

Let f(x) = 2x^2 + 3x and g(x) = 4x 1 Find g (f( 6)) =

Let f(x) = 2x^2 4x and g(x) = 3x 1 Find f (g(-1)) =

If f(x) = x + 7 and h(x) = 2x 5 , find a function g(x) such that g \circ f(x) = h(x).

Use the graphs of f and f^ 1 to complete each table of function values.

Use the given graphs of f and g to evaluate each expression (a) f(g(2)) (b) g(f(0)) (c) (fog)(0) (d) (gof)(6) (e) (gog)(-2) (f) (fof)(4)

Let f(x) = \sqrt{7 - 8x}. Which of the following decompositions of f(x) = p(q(x)) into a pair of functions p(x) (the outside function) and q(x) (the inside function) is/are correct? Select all that...

Let A = f(r) be the area of a circle with radius r and r = h(t) be the radius of the circle at time t. Which of the following statements correctly provides a practical interpretation of the composi...

If F(x) = f(g(x)), where f(-4) = 3, F(-4) = 5, F'(4) = 5, 9(4) = -4, and g'(4) = 3, find F '(4).

For the functions f(x)= x2 +1 and g(x)=10x +x+1 a) Find (f g)(x) b) Find the derivative (fog)' at the point of x=0.

If f:(X,d1) to (Y,d2) and g:(Y,d2) to (Z,d3) are continuous functions, prove that g composition f :(X,d1) to (Z,d3) is continuous.

Find the value of (f of g)' at the given value of x. f (u) = 6u / u^2 + 5, u = g (x) = 3 x^2 + 5 x + 1, x = 0

Let f x = 5 square root x and g x = 4 + cos x. a. Find f g x and f g' x b. Find g f x and g f' x

Let f x = x^5 and g x = 2x - 3. a. Find f g x and f g' x b. Find g f x and g f' x

The collection of people, technology, and systems within an organization that has primary responsibility for providing the organization's products or services is called _____. a. the supply chain b...

Let f(x) = \dfrac{2}{e^x} and g(x) = \dfrac{x}{x^2+1}. Find g \circ f, express the answer in rational function.

Let f(x) = sin(\sqrt{x}) and g(x) = 1-3x^2. Find g \circ f and give its domain.

Let f(x) = sin(\sqrt{x}) and g(x) = 1-3x^2. Find f \circ g and give its domain.

The Operations function refers to: a. Labor b. Transformative Processes c. Cost Allocation Process d. Capital Fundraising processes

Suppose f(x) = \sqrt{x} and g(x) = \sqrt[3]{1 x}. FInd f\circ g(x) , g \circ f(x) , and f\circ f(x).

Determine \displaystyle{ g \circ f (x) } where f(x) = 9x^2 11x and g(x) = 2\sqrt{x+2}.

Determine \displaystyle{ f \circ g (x) } where f(x) = 9x^2 11x and g(x) = 2\sqrt{x+2}.

For functions f(x) = 6^27ln(x)+10 and g(x) = -20/x, determine the composite function (g o f) (x).

For the given function, find the composite function. (a) v(x) = x^2-5x+4, t(x) = x-1, (v circ t)(2) (b) q(x) = 5x-3, (q circ q)(x)

For the given function, find the composite function. (a) g(x) = 5x-3, h(x) =x+1, (g circ h) (x) (b) f(x) = 4x-5/x+6, p(x) = 2-5x, (p circ f) (x)

Let f:Z Z and g : Z Z be functions defined respectively by Find g f and f g.

Given the two functions f(x)= 4x and g(x)=x -1, evaluate each composite function and find the domain and range of each function and determine f(g(x)).

Given the two functions f(x)= 4x and g(x)=x -1, evaluate each composite function and find the domain and range of each function and determine g(f(5)).

Given the two functions f(x)= 4x and g(x)=x -1, evaluate each composite function and find the domain and range of each function and determine (fg)(-4)

Given the two functions f(x)= 4x and g(x)=x -1, evaluate each composite function and find the domain and range of each function and determine g(1).

Given the two functions f(x)= 4x and g(x)=x -1, evaluate each composite function and find the domain and range of each function and determine f(g(1)).

Given that g(x) = x^2 + 3 and f(x) = x^2 + 5x + 7, what is f(g(x))?

Determine the limit if it exists, \displaystyle{ \lim\limits_{x \to 0^+} f(f(x)) } where the graph of the function f(x) is given below.

Let f (x) = 5 x^3 + 2, g (x) = 7 x^2 + 3 x. Compute f of g (x).

The price of a product is given by the following function: f(x) = 1 + \dfrac{4x}{x^2 + 4}. Calculate the following: f(-2).

A square concrete foundation is prepared as a base for a cylindrical tank (see figure). Find and interpret (A r)(x).

Let F(x, y, z) = (x^2y, sin z) and G (x, y) = (x y^2, e^x, cos y). Find (G of F)' (1, 2, pi).

Let f(x) = sin x and g(x) = cos x. Find the value of (f*g)(pi/3).

Suppose that f x = fraction x + 8 x - 3 and g x = fraction 2x - 1 x - 11. Find the exact value of the x-intercept of the function f g x .

Consider the graph of the parabola y=x^2+x in the x-y plane. A particle is moving at a constant speed of 3sqrt(26) along the graph of the parabola. Given that dx/dt is greater than 0 when a particl...

Evaluate each expression using the graphs of y=f(x) and y=g(x) shown below. IMAGE (a) (f\circ g)(-1) (b) (f\circ g)(4)

Evaluate each expression using the graphs of y=f(x) and y=g(x) shown below. IMAGE (a) (g\circ f)(-1) (b) (g\circ f)(0)

Evaluate each expression using the values given in the table. |x|-3| -2 |-1 |0 |1 |2 |3 |f(x)| -9| -6| -3 |-1| 3| 6| 9 |g(x)|7| 3| 0 |-1| 0| 3| 7 a. (g\circ f)(-1) b. (g\circ f)(0)

Evaluate each expression using the values given in the table. |x|-3| -2 |-1 |0 |1 |2 |3 |f(x)| -9| -6| -3 |-1| 3| 6| 9 |g(x)|7| 3| 0 |-1| 0| 3| 7 a. (f\circ g)(1) b. (f\circ g)(-1)

If f(x) = 3x^2 + 4 and g(x) = 2^x 3 find each of the following: a) \displaystyle{ A(x) = f(x) g(x). } b) \displaystyle{ B(x) = f (g(x)). } \displaystyle{ C(x)...

Let N(t) be the number of computer monitors a manufacturer has stored in its warehouse t weeks after the start of the year. If C(x) is the weekly cost the company incurs to store...

Let f(x) = 4/(2x + 1), g(x) = k*cot x, and k greater than -1 is a constant. Given that (fog)'(pi/4) = -16, then the value of k equals to _____.

Find the exact value of the following expression. sec (tan^-1 3 / 4)

Find the exact value of the following expression. tan (sec^-1 4)

Find dy/dt. y = cos(sqrt(4t + 11)).

Find the composite function f g h x for the following functions. f x = fraction 1 x+1 g x = square root x-1 x h x = x^2 + 1

Find the composite function f(g(h(x))) for the following functions: f(x) = 1/(x+1) g(x) = (\square root (x-1))/x h(x) = x^2 + 1

Find f of g of h. f (x) = x^4 + 6, g (x) = x - 8, h (x) = square root x

Define the function formula for each of the following given the function definitions for f, g, and h. f(x) = sqrt(x + 4), g(x) = 4x - 6, h(x) = 6x. A) f(g(x)) B) g(f(x)) C) h(f(x))

Define the function formula for each of the following given the function definitions for f, g, and h. f(x) = sqrt(x + 5), g(x) = 4x - 7, h(x) = 5x. A) f(g(x)) B) g(f(x)) C) h(f(x))

Find h(g(f(2))) given the function definitions for f, g, and h. f(x) = sqrt(x + 5), g(x) = 3x - 5, h(x) = 6x.

Find h x,y)= g f x,y and the set of points at which h is continuous. g t =t^2 +square root t, f x,y= 2x +3y-6

Use the graphs of f(x) and g(x) to evaluate the functions. f(x): g(x): (a) (f ο g)(1) (b) (g ο f)(3)

Use the graphs of f(x) and g(x) to evaluate the functions. f(x): g(x): (a) (f ο g)(2) (b) (g ο f)(2)

Consider f (x) = 5 x - 4 and g (x) = x^2 - 4. a. Compute: (f of g)(4). b. Compute: (g of f)(4). c. Compute: (f of g)(-3). d. Compute: (g of f)(-3).

How does particle size distribution affect the properties of composites?

Given f (x) = 1 / x - 4 and g (x) = 16 / x + 3, find the domain of f (g (x)).

Let f (x) = x^2 - x and g (x) = 2 x^2. Find the derivative of the composite function f(g(x)) that is a d / dx (f(g(x))).

Write sin^2 (e^x^2 - x) as a composition of (elementary) functions.

a. Write the composite function in the form f(g(x)). (Identify the inner function u = g(x) and the outer function y = f (u).) y = cube root of 1 + 7 x b. Find the derivative dy/dx.

Consider the following functions: f(x) = x^2 - 5x + 1, \; g(x) = 2x + 13. Find the value of (g \circ f)(5).

Suppose that f(x) = 2x + 1 and g (x) = x^2 - 3, then find (f of (f of g)) (x).

Given that f (x) = square root 1 - x^2 and g (x) = square root x - 5, find (f of g) (x) and its domain.

Suppose that f (x) = square root 5x, g (x) = x / x - 2 and h (x) = cube root 12 x. Find (f of g of h) (x).

If g(x) = 2x + 1 and h(x) = 4x^2 + 4x + 7, find f so that f o g=h.

Suppose f is even and g is odd. Is the function f o g odd too? Explain

Given that \displaystyle{ \begin{alignat}{3} f(x) &=&& \; \sqrt[3]{x 4}, \\ g(x) &=&& \; x^3 + 4, \end{alignat} } determine the value of the following if possible: \displaystyle{ (f...

Evaluate [fg]( 1) if \displaystyle{ \begin{alignat}{3} f(x) &=&& \; x^2 = 3, \\ g(x) &=&& \; x + 9. \end{alignat} }

Find (f \circ g) , if \displaystyle{ \begin{alignat}{3} f(x) &=&& \; x + 2, \\ g(x) &=&& \; x^2. \end{alignat} }

Let f(x) = 5x + 7 and g(x) = 7x 2 . Find (g \circ f)(8).

Let f (x) = 3 - square root x^2 + 1 and g (x) = x - 5. Determine (f of g) (x).

Assume f of g (x) = 1 / x - 7. If g (x) = x - 7, find the function f (x).

Fill in the blanks. The domain of ( f\circ g) is all \, x\, in the domain of \, g\, such that _______ is in the domain of \, f.

For the following pair of functions, find 1. (f of g) (x). 2. (g of f) (x). 3. The domain of (f of g) (x). 4. The range of (f of g) (x). f (x) = 1 / 1 - x, g (x) = square root 5 - x

Find the domain of f (x) = square root 1 - square root 1 - x^2 and express it as a composition of three functions. Note that a function can be used more than once.

Find f of g and g of f and state their domains if f (x) = 1 / x and g (x) = 2 x +1.

Identify the inside function, u = g(x) and the outside function, y = f(u). (Use non-identity functions for g(x) and f(u).) y = f(g(x)) = cube root 5 - x^2

If M(t) = t + square root t, N (t) = 2t + 5, C(t) = M(N(t)), and D(t) = N(M(t)), compute C(2) and D(4).

Find functions f and g so that h (x) = f(g (x)). h (x) = square root 2 x^2 + 8

Identify the inside function, u = g(x) and the outside function, y = f(u). (Use non-identity functions for g(x) and f(u).) y = f (g (x)) = 1 / square root x^2 - 6

Consider the following functions: f(x) = x^2 -3, \; g(x) = 2x + 2. Determine g \circ g and state its domain.

Consider the following functions: f(x) = x^2 -3, \; g(x) = 2x + 2. Determine f \circ f and state its domain.

Consider the following functions: f(x) = x^2 -3, \; g(x) = 2x + 2. Determine g \circ f and state its domain.

Identify the inside function, u = g(x), and the outside function, y = f(u). y = (x^2 - 2 x + 9)^2

Evaluate the following expression based on the graph of f(x). f(0)

Show that the Associative Property holds for compositions of functions-that is: \, (f\circ(g\circ h))(x) = ((f\circ g)\circ h)(x).\,

Use the graphs of f and g to graph h(x) = (f + g)(x). [{Image src='image_2022-06-10_1518421638725027109608159050.png' alt='' caption=''}]

Let f(x) = ln (x+2y-2) evaluate and simplify the expression f(0,1).

Let f(x) = ln (x+2y-2) evaluate and simplify the expression f(1,1).

If x=t^3-3t, y=3t^2-9, the find x and y for the t: -3, -2, 1, 0, 1, 2, 3.

Use the functions given by f(x) = 1/8 x - 3 and g(x)= x^3 to find the indicated value or function. (g^(-1) o g^(-1))(-4).

Consider the values in the table below. Find the slope of the tangent line to c(x) = e^{g(x)} at x= 0. | x | h(x) | g(x) | h'(x) | g'(x) | 0 | 2 | 1 | -5 | 4 | 1 | 4 | 2 | -4 | -2 | 2 | 3 | 0 | -2...

Consider the values in the table below. Let t(x) = \sqrt{h(x) + 2}. Find t'(0). | x | h(x) | g(x) | h'(x) | g'(x) | 0 | 2 | 1 | -5 | 4 | 1 | 4 | 2 | -4 | -2 | 2 | 3 | 0 | -2 | 3 | 3 | 0 | 1 | -3 | 2

The graph of \ y=f(x)\ is shown in the screenshot below. Sketch the following function: \ y=-2f(-x).

Find (a) (f + g)(x), (b) (f - g)(x), (c) (fg)(x), and (d) (f/g)(x). What is the domain of f/g? f(x) = (x)/(x + 1), g(x) = x^3.

How is the composite function f circ g defined? What is its domain?

Is it true that f circ (g + h) = f circ g + f circ h?

Consider the functions f(x) = x^2 and g(x) = \sqrt{x}. (a) Find f/g and its domain.

Determine whether the statement is true or false. Justify your answer. If you are given two functions f(x) and g(x), you can calculate

For the given functions f(x) and g(x), find the indicated composition (f dot g)(x): f(x)= sqrt(x-1) g(x)= -7/x

Determine whether (fog (x)=x and whether (fog(x)=x; f(x) =x^{2}+3, g(x)= \sqrt{x-3}.

Fill in the blanks. The _____ of the function f with g is (f\circ g)(x)=f(g(x)).

Find two functions f and g such that (f circle g)(x)= h(x). h(x) = Cube root of{x+2}

Find two functions f and g such that (f circle g)(x)= h(x). h(x) = (1-2x)^3

a. Parameterize a cone lying over the x, y plane with its tip at the point (3,4), height 3, and its maximum radius 6. b. Calculate the surface area of this cone. c. Calculate the integral G(x, y, z...

Consider the functions given by f (x) = sin x and f^-1 (x) = arcsin x. (a) Use a graphing utility to graph the composite functions f of f^-1 and f^-1 of f. (b) Explain why the graphs in part (a) a...

Express the function in the form f of g. F(x) = (2x + x^2)^4

Express the function in the form f of g. F (x) = cube root of x / 1 + cube root of x

Find fogoh. f(x) = tan x, g(x) = x/(x - 1), h(x) = cube root of x.

Find fogoh. f(x) = sqrt(x - 3), g(x) = x^2, h(x) = x^3 + 2.

Find two functions f and g such that (f of g)(x) = h(x). (There are many correct answers.) h (x) = (2x + 1)^2

Find (a) f of g, (b) g of f, and (c) g of g. f (x) = x^3, g (x) = 1 / x

Find (a) f of g, (b) g of f, and (c) g of g. f (x) = cube root x - 1, g (x) = x^3 + 1

Find (a) f of g, (b) g of f, and (c) g of g. f (x) = 3 x + 5, g (x) = 5 - x

Find (a) f of g and (b) g of f. Find the domain of each function and each composite function. f (x) = x^2/3, g (x) = x^6

Find (a) f of g and (b) g of f. Find the domain of each function and each composite function. f (x) = 1 / x, g (x) = x + 3

If f (x) = x^2 + 1, g (x) = square root x, find (a) f of g and (b) g of f. Find the domain of each function and each composite function.

For the following piecewise function f(x) = -3x + 2 for x > 4, f(x) = x - 1 for 0 < x < 4 and f(x) = -5 for x < 0, solve for f(f(3)).

Let f(x) = 1/x and g(x) = 1/x^2. (a) Find (f degree g)(x). (b) Is f degree g continuous everywhere? Explain.

Find fogoh. f(x) = absolute of (x - 4), g(x) = 2^x, h(x) = sqrt x.

Find fogoh. f(x) = 3x - 2, g(x) = sin x, h(x) = x^2.

Find the functions (a) fog, (b) gof, (c) fof, and (d) gog and their domains. f(x) = x/(1 + x), g(x) = sin 2x.

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