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!