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

Answer:

a. 40

Step-by-step 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.