## Skills Review for Substitution and Integrals Involving Exponential and Logarithmic Functions

### Learning Outcomes

• Decompose a composite function into its component functions

In the Substitution and Integrals Involving Exponential and Logarithmic Functions sections, we will learn all about using substitution as an integration method. Substitution is basically the process used to find the antiderivative of a function that was differentiated using the chain rule. That being said, it is important to be able to look at a composite function and identify the inside function and outside function. Usually, the inside function is what we set our substitution variable equal to.

## Identify Components of Composite 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.

### Example: Identifying Components of Composite Functions

Write $f\left(x\right)=\sqrt{5-{x}^{2}}$ as the composition of two functions.

### Example: Identifying Components of Composite Functions

Write $f\left(x\right)=e^{4x-3}$ as the composition of two functions.

### Try It

Write $f\left(x\right)=\dfrac{4}{3-\sqrt{4+{x}^{2}}}$ as the composition of two functions.