Composition of functions

Math

Definition

Composition of functions is the process of applying one function to the result of another. Written as (f ∘ g)(x) = f(g(x)), you first evaluate the inner function g(x), then use that output as the input for f.

How It Works

  1. Identify the inner function g(x) and outer function f(x)
  2. Substitute g(x) into every x in f(x)
  3. Simplify the resulting expression

Examples

  • If f(x) = 2x + 1 and g(x) = x², then f(g(3)) = f(9) = 19
  • A store applies a 20% discount then 8% tax — that's a composition of two functions
  • Converting Celsius to Fahrenheit, then Fahrenheit to Rankine

Related Terms

Function notation Inverse functions Domain and range Chain rule

Study This Concept

Practice composition of functions with free review games in these units:

Pre-Calculus Unit 1: Functions and Their Graphs