Question

Please help! functions operations. explain please

Answer 1

Hello!

The answer is: a. 40

Why?

We are working with composite functions, so, to find the correct option, first we need to follow the composite function process:

`(h\circ g)=h(g(x))`

So,

We are given the functions:

`g(x)=2x\\\\h(x)=x^(2)+4`

So,

`(h\circ g)(x)=(2x)^(2)+4`

Then, evaluating with "x" equal to -3, we have:

`(h\circ g)(-3)=(2*-3)^(2)+4=(-6)^(2)+4=36+4=40`

So, the correct option is a. 40

Have a nice day!

Answer 2

a. 40

Explanation:

Given

`g(x)=2x` and
`h(x)=x^2+4`

`(h\circ g)(x)=h(g(x))`

`(h\circ g)(x)=h(2x)`

We plug in 2x into
`h(x)=x^2+4`.

`(h\circ g)(x)=(2x)^2+4`

`(h\circ g)(x)=4x^2+4`

We now substitute x=-3.

`(h\circ g)(-3)=4(-3)^2+4`

`(h\circ g)(-3)=36+4=40`

The correct choice is A.