Question

Help meeeeeeeeeeee pleaseeeeeeeeeeeeee!!

Answer 1

Solutions below.

Explanation:

This question tests on the concept of Composite Functions

Composite Functions

Composite functions are functions that is derived from another new and separate function.

Example: f(x) = 5x, g(x) = 9x , (f • g)(x) = f(g(x)) = f(9x) = 5(9x) = 45x

Application

Given to us are 2 functions:

f(x) =

`{x}^(2) - 7x + 4`

g(x) =

`- 2x`

We are asked to find (f • g)(4). We first find (f • g)(x).

(f • g)(x) = f(g(x)) = f(-2x) =

`{( - 2x)}^(2) - 7( - 2x) + 4 \\ = 4 {x}^(2) + 14x + 4 \\ = 2(2 {x}^(2) + 7x + 2)`

Now, we will find the value of (f • g)(4) by substituting x = 4 into (f • g)(x).

(f • g)(4) =

`2(2 {(4)}^(2) + 7(4) + 2) \\ = 2(2(16) + 28 + 2) \\ = 2(32 + 28 + 2) \\ = 2(62) \\ = 124`