Determine if the statement is true or false given f(x) = 2(1.2^x) and g(x) = x^2 + 4. f(x)...
Question:
Determine if the statement is true or false given {eq}f(x) = 2(1.2^x) {/eq} and {eq}g(x) = x^2 + 4 {/eq}.
{eq}f(x) > g(x)\; \text{for}\; 0 < x < 8 {/eq}
Verifying Mathematical Statements:
To verify a math statement, we consider the given conditions. If applying the given conditions to the statement corresponds to the statement, then it is a true statement. If it contradicts to the statement, then the statement is false.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerWe determine whether the statement {eq}f(x) > g(x) {/eq} for {eq}0 < x < 8 {/eq} is true or false given the functions:
- {eq}f(x) =...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Writing and Classifying True, False and Open Statements in Math
from
Chapter 2 / Lesson 5
44K
When writing and classifying statements in math, it is important to know what is true, false, or open. Study the definition of true, false, and open statements, and learn how to write and classify them.
Related to this Question
- 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'(x) = g'(x) for 0 less than x less than 1, then f(x) = g(x) for 0 less than x less than 1.
- True or false, explain. If f'(x) = g'(x) for 0 less than x less than 1, then f(x) = g(x) for 0 less than x less than 1.
- Determine if the statement is true or false given f(x) = 2(1.2^x) and g(x) = x^2 + 4. f(x) greater than g(x)\; \text{for}\; |x| \leq 2
- Determine whether the statement is true or false given that f(x) = ln x. If f(x) less than 0, then 0 less than x less than 1.
- There is a function g such that g(-1) = -3, g(2) = 5 and g'(x) is less than 0 for all x in Real Number. True or false?
- For the function f given above, determine whether the following conditions are true. Write T for true and F for false. i. f'(x) is less than 0 if 0 is less than xis less than 2; ii. f'(x) is greate
- Consider the function f(x) = {0, x = 0 and 1 - x, 0 less than x less than equal to 1}. Which of the following statements is false? a. f is differentiable on (0, 1). b. f(0) = f(1) c. f is continuous
- Determine if the statement is true or false given f(x) = 2(1.2^x) and g(x) = x^2 + 4. \text{As}\; x \rightarrow -\infty,\; g(x) greater than f(x)
- Determine if the statement is true or false given f(x) = 2(1.2^x) and g(x) = x^2 + 4. \text{As}\; x \rightarrow \infty,\; f(x) greater than g(x)
- Determine if the statement is true or false given f(x) = 2(1.2^x) and g(x) = x^2 + 4. \text{As}\; x \rightarrow 0,\; g(x) greater than f(x)
- Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If F'(x) = G'(x) on the interval ~[a, b], then F(b) - F(a) = G(b)- G(a).
- There is a function f such that f(0) = -1, f(1) = 4 and f'(x) less than 0 for all x in real number. True or false?
- Determine whether the statement is true or false. If {f}'(x) > 0 for 6 < x < 8, then f is increasing on (6, 8).
- Determine if the statement is true or false given f(x) = 2(1.2^x) and g(x) = x^2 + 4. g(x) greater than f(x)\; \text{for}\; x \leq 0
- If f'(x) = g'(x) then f(x) = g(x). a) true b) false Why?
- True or False: If f'(x) less than 0 for all x in (0,1), then f(x) is decreasing on (0,1).
- True or False. If False, explain why. The function f(x) = { x 2 x greater then 0 x 2 1 x less than 0 has a local minimum.
- Indicate whether the statement is true or false. If the statement is false, provide a counterexample. There exists a function f such that f(1) = -2, f(5) = 6, and f'(x) less than 2 for all x.
- 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. There exists a function f such that f(x) less than 0, f'(x) less than 0, and f''(x) greater than 0 f
- Determine if the following statement is true or false: If f(x) = \sum_{n=0}^{\infty} a_n \: x^n for all x, then f'(x) = \sum_{n=0}^{\infty} n \: a_n \: x^{n-1} for all x.
- Indicate whether the following statement is either true or false. If true, explain how you know. If it is false, explain how you know or provide a counterexample (an example that shows the statement is false). If f'(x) = g'(x) for 0 less than x less than
- Determine whether the following statement is true or false. The function f(x,y) = \left\{\begin{matrix} \frac{x^{2} + x^{4}y + y^{6} +y^{7{x^{2} + y^{6& if (x,y) \neq 0 \\ 1 & if (x,y) = 0 \\ \end{matrix}\right. is continuous at the point (0,0).
- Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f is increasing on (a, b), then the minimum value of f (x) on (a, b) is f (a).
- Suppose the derivative of a function of f is f'(x) = (x + 1)^2(x - 5)^5(x - 6)^4. Then f is decreasing on (-\infty,-1) and (-1, 5). True False
- Determine if the following statements are true or false. If the statement is false give a counterexample or explain why. 1. Where a function f is decreasing, its associated slope function f' is negat
- Determine whether the following statement is true or false: If f and g are differentiable, then \dfrac{d}{dx} f(g(x)) = f'(g(x))g'(x).
- 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 x_1 less than x_2 and f is a decreasing function, then f(x_1) greater than f(x_2).
- If f'(x) and g'(x) exist and f'(x) greater than g'(x) for all real x, then the graph of y = f(x) and the graph of y = g(x) intersect no more than once. True or false?
- Determine whether the following statement is true or false and give an explanation or a counterexample: A function ''f'' has the property that f'(2) = 0. Therefore, ''f'' has a local maximum or minimum at x = 2.
- Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f'(x) greater than 0 for all real numbers x, then f increases without bound.
- If f(x) = frac(x^2 4)(x-2) and g(x) = x + 2 then we can say the functions f and g are equal. a. True b. False
- Determine whether each statement is true or false. f has an absolute minimum at ='false' (a, b), if f (x, y) \geq f(a, b) for all point (x, y) in the domain of f. True = False =
- Explain whether the statement is true or false. Justify your answer. If f'(x) = g'(x), then f(x) = g(x).
- Determine whether the statement is true or false. If f and g are functions such that \displaystyle \lim_{x \to 0} f(x) = \displaystyle \lim_{x \to 0} g(x), then f and g must have the same y-intercept.
- Determine whether the statement that follows is true or false. If the statement is true, explain why. If a statement is false, provide a counterexample. True or False: lim_(x to 0) f'(x) = (f(x + h) - f(x))/h
- Determine whether the statement that follows is true or false. If the statement is true, explain why. If a statement is false, provide a counterexample. True or False: f'(x) = (f(x + h) - f(x))/h
- 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 differentiable and f(x) greater than or equal to g(x) for a less than x less than b,
- The graph of f'(x) is continuous, positive and has a relative maximum at x = 0. Determine if the following statement is true or false: The graph of f has a relative minimum at x = 0.
- True or False? Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f(x) \lt g(x) for all x \ne a, then \lim\limits_{x\ \to\ a} f(x) \lt \lim\limits_{x\ \to\ a} g(x).
- State whether the following statement is true or false. \int_0^\pi f(x) \cos x dx = - \int_0^\pi f'(x) \sin x dx
- State whether the following is true or false. If f'' less than 0, then f is concave up on that interval.
- Is the following statement true or false: Suppose a greater than 0, and let f is a function defined on (a ,+ ), define g(x) = f(1x) for 0 less than x less than 1/a. Then lim x f(x) exists if and only if lim x 0 g(x) exists.
- True or false? The function is decreasing. f(x) = 7e^x
- True or false? The function is decreasing. f(x) = x^5 + 6x + 2
- True or false? The function is decreasing. f(x) = 4\ln x
- Determine whether the statement is true or false given that f(x) = ln x, where x > 0. Justify your answer. If f (x) > 0, then x > e.
- Determine whether the statement is true or false given that f(x) = ln x, where x > 0. Justify your answer. f(x - a) = f(x) - f(a), x > a
- Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The relative maxima of the function f are f(1) = 4 and f(3) = 10. So, f has at least one minimum for some x in the interval (1, 3).
- 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 x1 < x2 and f is a decreasing function, then f(x1) > f(x2).
- True or false? If f'(x) and g'(x) exist and f'(x) greater than g'(x) for all real x, then the graph of y = f(x) and the graph of y = g(x) intersect no more than once.
- Determine whether the following statement is true or false. If false, explain why. Because 3+5i is a zero of f(x)= x^2-6x+34, we can conclude that 3-5i is also a zero. Is the statement true or false?
- True or false: If f'(x) <0 for all x ln(0,1), then f(x) is decreasing on (0,1).
- Determine whether the statement is true or false given that f(x) = ln x, where x > 0. Justify your answer. If f (x) < 0, then 0 < x < e.
- Find: If f'(x) is increasing, then f(x) is also increasing true or false and why
- Determine whether the statement is true or false given that f(x) = ln x. square root f (x) = 1 / 2 f (x)
- Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If f ''(x) less than 0 for all real numbers x, then f decreases without bound.
- Determine whether the statement is true or false. If f and g are functions such that the limit as x approaches 0 of f(x) = the limit as x approaches 0 of g(x), then f and g must have the same y-intercept.
- The graph of f'(x) is continuous, positive and has a relative maximum at x = 0. Determine if the following statement is true or false: The graph of the function is always increasing.
- Determine if the following statement is true or false. A) If f(x) = 3x^5 - 5x^3, then f(x) has a real minimum at x = 1. B) If f(x) = 3x^5 - 5x^3, then f(x) has an inflection point at x = 0.
- State True or False. If a differentiable function f has a minimum or maximum at x = c, then f' (c) = 0.
- 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 g(x) = x^5, then \lim_{x \to 2} \dfrac{g(x) - g(2)}{x - 2} = 80
- Determine if the following statement is true or false. If f(x) less than g(x), for all x is not equal to c, then the limit as x approaches c of f(x) less than the limit as x approaches c of g(x).
- True or False? For any integral function f , c a f(x) dx = b a f(x) dx + c b f(x) dx where a less than b less than c .
- __True or False?__ Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If \ f'(x) = 0 for all x in the domain of f, then f is a constant function.
- Determine whether the following statement is true or false: If g(x) = x^3, then \lim_{x \to 2} \dfrac{g(x) - g(2)}{x-2} = 12.
- There is a function f such that f(-1) = 2, f(0) = -1 and f'(0) greater than 0 for all x in real number. True or false?
- State True or false If f ( x ) less than g ( x ) for all x \neq c , then \operatorname { lim } _ { x \rightarrow c } f ( x ) | less than \operatorname { lim } _ { x \rightarrow c } g ( x ) |
- Determine whether the statement is true or false. Suppose that g(x) = f(x) \sec x, where f(0) = 5 and f'(0) = -3. Then \begin{align} g'(0) &= \lim_{h \to 0} \dfrac{f(h)\sec h - f(0)}{h} \\ &= \lim_{h \to 0} \dfrac{5(\sec h - 1)}{h} \\ &= 5\dfrac{d}{dx}\l
- The derivative of (g(x))' is g''(x). True or false?
- If g(x) is a vertical shift of f(x), then f'(x) = g'(x) true or false and why?
- Determine whether the following statement is true or false. If f has an absolute minimum value at c, then f double prime(c) = 0.
- Determine whether the following statement is true or false and give an explanation or a counterexample: The function f(x) = \sqrt{x} has a local minimum on the interval \left 0, \infty \right ).
- The domain of the function f(x) = \frac{x^{2} - 4}{x} is (-\infty, -2) \cup (-2,2) \cup(2,\infty). True False
- "If f'(x) and g'(x) exist and f'(x) > g'(x) for all real x, then the graph of y=f(x) and the graph of y=g(x) intersect exactly once. Select one: True or False?"
- Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. If a function is continuous on a closed interval, then it must have a minimum on the interval.
- TRUE or FALSE a) If f is an increasing function and g is an increasing function, then (f cdot g) is an increasing function. b) If f is increasing for all x in it's domain, then f cannot ha
- Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The maximum slope of the graph of y = sin(b x) is b.
- Indicate whether the statement is true or false: The derivative of a polynomial function is always another polynomial function.
- 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 is continuous on [a, b] and f(x) [{MathJax fullWidth='false' \geq }] 0, then
- The function f(x) = 1 / {ln (x^2)} is guaranteed to have an absolute maximum and minimum on the interval (-5, -1). a. True. b. False.
- Determine whether the statement is true or false. The graph of y = f(-x) is a reflection of the graph of y = f(x) in the x-axis.
- Suppose ='false' f(x, y)=xy+8|. Compute the following values: ='false' f(x+2y, x-2y)=\Box ='false' f(xy, 3x^2y^3)=\Box
- Determine whether the statement is true or false. If it is false, explain why or give an example that shows it is false. The graph of f (x) = 1 /x is concave downward for x less than 0 and concave upward for x greater than 0, and thus it has a point of in
- Determine whether the statement is true or false. If (7x + 4) is a factor of some polynomial function f, then 4 / 7 is a zero of f.
- State true or false. The domain of the function f(x) = In(x) is (- infinity, infinity)
- If f'(x) and g'(x) exist and f'(x) is greater than g'(x) for all real x, then the graph of y = f(x) and the graph of y = g(x) intersect not more than once. True or false?
- If f'(x) and g'(x) exist and f'(x) is greater than g'(x) for all real x, then the graph of y = f(x) and the graph of y = g(x) intersect exactly once. True or false?
- A function f is graphed below. Let g(x)= \int_{-2}^x f(t) dt. Decide whether the following statements about g are true or false. a. g is increasing on (-1,1.5) b. g(-1)=1 c. g(2)=4 d. g has an inflection point at x=1
- Determine whether the statement is true or false. If a, b, and c are real numbers, and a less than or equal to b, then ac less than or equal to bc.
- 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 0 less than a less than b, then ln a less than ln b.
- True or False? If f (x) less than 0 and f"(x) greater than 0 for all x then f is concave down.
- 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 increasing on an interval I, then f - g is increasing on I.
- True or False: If "f" and "g" are differentable and f(x)> or equal to g(x) for a<x<b, then f' (x)> or equal to g'(x) for a<x<b.
- Indicate whether the statement is true or false. If the statement is false, provide a counterexample. Suppose f'(x) exists on (-2,3) and f'(0) = 0. Then f is not increasing on (-2,3).
- Determine whether the following statement is true or false: The function given by f(x)= -12x^2- 1 has no x-intercepts.
- True or False: If f(x) is differentiable and concave up for all x, then f'(a) less than \frac{f(b)-f(a)}{b-a}; a less than b.
- Evaluate the following as true or false. if f"(x) 0 and f'(x) equals 0 at the point (x, f(x)), then the point must be a relative maximum.
- The graph of f'(x) is continuous, positive and has a relative maximum at x = 0. Determine if the following statement is true or false: The graph of f has a relative maximum at x = 0.
- 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 increasing on an interval l, then f + g is increasing on l.
- Consider the function f(x) below. Considering the intermediate value theorem and the vertical asymptote at x=0, is the following statement true or false? For any number C greater than 0, there is a positive value of x that satisfies the equation f(x)=C.
Explore our homework questions and answers library
Browse
by subject