Finding Composite Functions

A composite function is one that obtained by plugging in an inner function into an outer function. In other words, a function takes the place of the independent variable in an outer function. To understand this concept, consider two functions f and g. Then, the composite function is denoted by f ◦ g which is defined by:

In other words, the function g is plugged into the function f.

To understand how to find composite functions, we will look at a few examples. 

Example 1:

It is also possible to have a composite function of three or more functions. The same rules of the previous examples apply. An example is shown next.

Example 2: