# For f(x) = x + 3 and g(x) = 4x + 2, find the following functions. a. (f \cdot g)(x) \\ b. (g...

## Question:

For f(x) = x + 3 and g(x) = 4x + 2, find the following functions.

{eq}a. (f \cdot g)(x) \\ b. (g \cdot f)(x) \\ c. (f \cdot g)(0) \\ d. (g \cdot f)(0) {/eq}

## Compositions of Functions

We can combine existing functions in order to construct new ones. One type of combination is called a composition, and it's constructed when we evaluate one function inside of another.

{eq}(f \circ g)(x) = f(g(x)) {/eq}

## Answer and Explanation: 1

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a. In order to construct this composition, we need to evaluate the function f at g. This means that we need to use g as the input in f. This gives us...

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