Question

Find the following
(u•w)(2)=
(w•u)(2)=

Answer 1

`(u \circ w)(2) = -34`

`(w \circ u) = -49`

Explanation:

We are given these following functions:

`u(x) = 4x + 2`

`w(x) = -5x + 1`

The first step to solve this question is finding the composite functions. So

`(u \circ w)(x) = u(w(x)) = u(-5x+1) = 4(-5x + 1) + 2 = -20x + 6`

`(w \circ u)(x) = w(u(x)) = w(4x + 2) = -5(4x+2) + 1 = -20x - 9`

At x = 2

Now we replace x by 2 in each of the functions. So

`(u \circ w)(2) = -20(2) + 6 = -40 + 6 = -34`

`(w \circ u)(2) = -20(2) - 9 = -40 - 9 = -49`