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 the free Mathway calculator and problem solver below to practice various math topics. Try the given examples, or type in your own problem and check your answer with the step-by-step explanations.

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