Question

O GRAPHS AND FUNCTIONSIntroduction to the composition of two functions

Answer 1

To answer this question, first of all, we need to find the composition of the two given functions:

The function r(x) = -2x²-2.

The function q(x)= 2x - 1.

The composition is given by:

`r\circ q(x)=r(q(x))`

Then, we have:

`r\circ q(x)=-2(2x-1)^2-2`

Expanding and simplifying, we have:

`r\circ q(x)=-2((2x)^2-2(2x)(-1)+(-1)^2)-2`
`r\circ q(x)=-2(4x^2+4x+1)-2=-8x^2_{}-8x-2-2`

Finally

`r\circ q(x)=-8x^2-8x-4`

Since we are asked for:

`r(q(-2))\Rightarrow r\circ q(-2)=-8(-2)^2-8(-2)-4`

Then

`r(q(-2))=-8(4)+16-4=-32+16-4=-20\Rightarrow r(q(-2))=-20`

In summary, the answer is:

`r(q(-2))=-20`