## Finding the Domain of a Composite Function

In this section, you will learn how to define the domain of a composite function.

### Decomposing a Composite Function into its Component Functions

In some cases, it is necessary to decompose a complicated function. In other words, we can write it as a composition of two simpler functions. There may be more than one way to decompose a composite function, so we may choose the decomposition that appears to be most expedient.

#### EXAMPLE 10

##### Decomposing a Function

Write as the composition of two functions.

##### Solution

We are looking for two functions, and , so . To do this, we look for a function inside a function in the formula for . As one possibility, we might notice that the expression is the inside of the square root. We could then decompose the function as

We can check our answer by recomposing the functions.