Learning Objectives:

__Math Tutoring on ____Determining Composite Functions and Composite Function Values__

A **Composite Function** can be thought of as a combination of two **functions**. The formal definition of a **composite function** states, given two **functions** **f** and **g**, the **composite function** denoted using this notation **f o g**.

This is read as " **f** composed with **g** " or just " **f of g**"

**f o g = ( f o g ) ( x ) = f ( g ( x ) ) . **

If** ( f o g ) ( x ) = ( g o f ) ( x ) = x** , then the two **functions** have a special relationship. They are Inverses of one another.

The Domain of **f ( g (x ) )** must contain the restrictions of the domain of **g ( x )** and the **composite functions**.

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**Hook Questions:**

*1. **What is a composite function?*

*2. **When did two functions call inverse of one another?*

*3. **What is the domain of f ( g (x) ) ?*

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