1 Answer

Will Mason · Answer 1 · 2023-10-12T13:39:53+0000

Answer:

Steps below.

Explanation:

This question tests on the concept of Composite Functions

Composite Functions

Composite Functions are functions derived from another separate function.

Example: f(x) = 4x, g(x) = 7x

(f • g)(x) = f(g(x)) = 4(7x) = 28x

Given from the Question:

$f(x) = {x}^(2) + 2$

and

g(x) = 4x

Using the above concept, we can solve for:

(f • g)(x) = f(g(x)) = f(4x) =

${(4x)}^(2) + 2 \\ = 16 {x}^(2) + 2 \\ = 2(8 {x}^(2) + 1)$

(g • f)(x) = g(f(x)) =

$g( {x}^(2) + 2) = 4( {x}^(2) + 2) \\ = 4 {x}^(2) + 8 \\ = 4( {x}^(2) + 2)$