Question

Composite functions 65 points helpppppp

Answer 1

`4√(x+2) - 6`

Explanation:

f(g(7)) = f(sqrt(x+2))

=4(sqrtx+2) - 6)

=
`4√(x+2) - 6`

Answer 2

`(f \circ g)(7)=6`

Explanation:

Given functions:

`\begin{cases}f(x)=4x-6\\g(x)=√(x+2)\end{cases}`

(f o g)(x) is a composite function.

Composite functions are when the output of one function is used as the input of another.

Therefore, the given composite function (f o g)(7) means to substitute the function g(x) when x=7 in place of the x in function f(x).

`\begin{aligned}\implies (f \circ g)(7)&=f[g(7)]\\& = f(√(7+2))\\&=f(√(9))\\&=f(3)\\&=4(3)-6\\&=12-6\\&=6\end{aligned}`