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:
[tex]r\circ q(x)=r(q(x))[/tex]
Then, we have:
[tex]r\circ q(x)=-2(2x-1)^2-2[/tex]
Expanding and simplifying, we have:
[tex]r\circ q(x)=-2((2x)^2-2(2x)(-1)+(-1)^2)-2[/tex][tex]r\circ q(x)=-2(4x^2+4x+1)-2=-8x^2_{}-8x-2-2[/tex]
Finally
[tex]r\circ q(x)=-8x^2-8x-4[/tex]
Since we are asked for:
[tex]r(q(-2))\Rightarrow r\circ q(-2)=-8(-2)^2-8(-2)-4[/tex]
Then
[tex]r(q(-2))=-8(4)+16-4=-32+16-4=-20\Rightarrow r(q(-2))=-20[/tex]
In summary, the answer is:
[tex]r(q(-2))=-20[/tex]
