p(x)=2x + 2 q(x)= -2x^2 + 1

Question

(q • p)(-1) =

(p • q) (-1) =

It’s finding the composition of two functions.

Answer 1

The easiest way to find the composition of two functions, evaluated at an input value, is to find the evaluation of the first function at the input value, retrieve that answer, then evaluate the next function at that new value.

So for the functions p(x)=2x+2 and q(x)= -2x²+1:

1.) (q • p)(-1)

First, find p(-1), since "p" is the function closest to the input value of -1:

p(-1) = 2(-1)+2 = -2+2 = 0

Secondly, take this new value and evaluate the next function, or find q(0):

q(0) = -2*(0)²+1 = -2*(0)+1 = 0+1 = 1. Therefore, (q • p)(-1) = 1

2.) (p • q)(-1)

First, find q(-1), since "p" is the function closest to the input value of -1:

q(-1) = -2*(-1)²+1 = -2*(1)+1 = -2+1 = -1

Secondly, take this new value and evaluate the next function, or find p(-1):

p(-1) = 2(-1)+2 = -2+2 = 0. Therefore, (p • q)(-1) = 0