Question

Find (g•f)(3)
f(x) = |x + 2|
g(x)=-x^2

Answer 1

-25

Explanation:

This question is asking for a composite function.

Let's take this step-by-step!

`f(x) = |x + 2|\\g(x) = -x^2`

(g•f)(3) means
`g(f(3))`

In English, this means we put 3 into f(x), and use the result for g(x).

First let's do f(x):

`f(3) = |3 + 2| = |5| = 5`

The lines mean "modulus"/"absolute value" which makes any number positive

For example,

`|-3| = 3`

`f(3) = 5\\g(f(3)) = g(5)\\g(5) = -(5)^2 = -25`