Question

52 points helppp composite functions give most simplified answer

Answer 1

(f∘g)(24) = -36

Explanation:

Pre-Solving

Given

We are given f(x) = -9x + 9 and
`g(x)= √(x+1)`.

We want to find (f∘g)(24).

This means that we first want to find g(24), then substitute the value of that into f(x).

Solving

Start by substituting 24 for x in g(x).

`g(24)= √(24+1)`

Add 24 and 1 together.

`g(24)= √(25)`

Take the square root of 25.

g(24) = 5

Now, substitute 5 as x in f(x) = -9x + 9.

f(5) = -9(5) + 9

Multiply.

f(5) = -45 + 9

Add the numbers together.

f(5) = -36

f(5) in this case has the same value as (f∘g)(24)

This means that (f∘g)(24) = -36

Answer 2

`(f \circ g)(24)=-36`

Explanation:

Given functions:

`\begin{cases}f(x)=-9x+9\\g(x)=√(x+1)\end{cases}`

Function Composition is applying one function to the results of another.

The composite function (f o g)(x) means to substitute the function g(x) in place of the x in function f(x).

Therefore (f o g)(24) means to substitute the result of g(24) in place of the x in the function f(x).

Calculate g(24) by substituting x = 24 into function g(x):

`\begin{aligned}\implies g(24)&=√(24+1)\\&=√(25)\\&=5 \end{aligned}`

Therefore:

`\begin{aligned}\implies (f \circ g)(24) & = f[g(24)]\\& = f(5)\\& = -9(5)+9\\&=-45+9\\&=-36\end{aligned}`