# Composite Function

## Topic

Functions and Relations

## Definition

A composite function is a function that is formed when one function is applied to the result of another function.

## Description

Composite functions are significant in mathematics because they allow the combination of two functions to form a new function. This is denoted as (f∘g)(x) = f(g(x)). Composite functions are widely used in various fields, including computer science for function composition in programming and in calculus for chain rule applications. For example, if f(x) = 2x and g(x) = x + 3, then the composite function

(f∘g)(x) = f(g(x)) = 2(x + 3) = 2x+6

Understanding composite functions is crucial for solving complex mathematical problems and for the analysis of functions in higher mathematics.

For a complete collection of terms related to functions and relations click on this link: Functions and Relations Collection

Common Core Standards CCSS.MATH.CONTENT.8.F.A.1, CCSS.MATH.CONTENT.8.F.B.5, CCSS.MATH.CONTENT.HSF.IF.A.1, CCSS.MATH.CONTENT.HSF.IF.A.2, CCSS.MATH.CONTENT.HSF.IF.C.7, CCSS.MATH.CONTENT.HSF.BF.A.1, CCSS.MATH.CONTENT.HSF.BF.B.3, CCSS.MATH.CONTENT.HSF.BF.B.4 6 - 9 Algebra     • Functions and Relations         • Composite Functions 2021 definition, function, relations, glossary terms