We discuss compositions of functions.

Given two functions, we can compose them. Let’s give an example in a ‘‘real context.’’

Composition of functions can be thought of as putting one function inside another. We use the notation

Now let’s try an example with a more restricted domain.

Compare and contrast the previous two examples. We used the same functions for each example, but composed them in different ways. The resulting compositions are not only different, they have different domains!

Many functions that you will encounter in math are actually a composition of functions, and you will need to recognize which functions they are composed of. Let’s practice this.

The function is a composition of which of the following functions? (Select all that apply)

Now that you know is composed of and , choose which composition results in .

The function is a composition of which of the following functions? (Select all that apply)

Hint:

Now that you know is composed of , , and , choose which composition results in .

The function is a composition of which of the following functions? (Select all that apply)

Now that you know is composed of , , and , choose which composition results in .