Composition of two functions

Question

Suppose that the following functions q and r are defined as follows. 

q(x)=-x-4

r(x)=4x+5

Find the following.

(q r)(-4)=

(r q)(-4)=

Answer 1

q(r(x)) = -(4x+5) - 4 = -4x - 5 - 4 = -4x - 9 ---> q(r(-4)) = 7

r(q(x)) = 4(-x-4) +5 = -4x-16+5 = -4x -11 ---> r(q(-4)) = 5

s=r*q=q*r = (-x-4)(4x+5) = -4x^2 - 5x - 16x - 20 = -4x^2 -21x - 20

s(-4) = -4(-4)^2 -21(-4) - 20 = -4(16) -21(-4) - 20 = -64 + 84 - 20 = 0