Composite Functions

Examples, worksheets, solutions, and activities to help PreCalculus students learn about composite functions.

What is a Composite Function?
Given two functions f and g, the composite function denoted by f ○ g.
This is read as “f composed with g” or “f of g”
f ○ g = (f ○ g)(x) = f(g(x))

This video defines a composite function and shows how to determine the value of a composite function and how to determine a composite function given two functions.

Learn how to calculate the compositions of two functions, including f(g(x)), g(f(x)), f(f(x)), and g(g(x)). Then describe the domain of each composite function.

Composition of Functions
Numerous examples are shown of how to compose functions

Composite Functions
This lesson explains the concept of composite functions. An example is given demonstrating how to work algebraically with composite functions and another example involves an application that uses the composition of functions.

Try out our new and fun Fraction Concoction Game.

Add and subtract fractions to make exciting fraction concoctions following a recipe. There are four levels of difficulty: Easy, medium, hard and insane. Practice the basics of fraction addition and subtraction or challenge yourself with the insane level.

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