Question

The functions r and s are defined as follows.
r(x)= 2x+2
s(x)= -2x^2-2

Find the value of s(r(4)).

I have no clue how to do this someone please help!

Answer 1

This is a problem of composition of functions. So, we have the following equations:

$r(x)=2x+2$
$s(x)=-2x^{2}-2$

First of all, we find the value of r(4), that is, substituting x = 4 in the equation we have:

$r(4)=2(4)+2=10$

Then we find s(r(4)) that is equal to s(10), therefore substituting x = 10 in the equation we have:

$s(r(4))=s(10)=-2(10)^{2}-2=\boxed{-202}$