Composite function

Composite functions are where one function is put inside of another. This can look intimidating at first, but these problems are quite simple once a student gets the hang of it.

Inside Out

It’s easiest to think of composite functions as a priority list or an order of operations. Work from the inside to the outside.

Here is an example from the June 2020 ACT:

Working from the inside out. g(−1) = (−1)² − 1  = 1 − 1 = 0. Since g(−1) = 0, g(−1) can be replaced with 0, as if it was a variable that we had solved for and could now plug into an equation.

Now the next layer: f(0) = 2(0)  + 3 = 3. The answer is 3!