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Math Tutorial 16.4 - Composite Functions

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There are 9 lessons in this math tutorial covering Composite Functions. The tutorial starts with an introduction to Composite Functions and is then followed with a list of the separate lessons, the tutorial is designed to be read in order but you can skip to a specific lesson or return to recover a specific math lesson as required to build your math knowledge of Composite Functions. you can access all the lessons from this tutorial below.

In this Math tutorial, you will learn:

  • What is a composite function?
  • How to express a composite function?
  • How to combine two or more functions to obtain a single composite function?
  • What are the properties of composite functions?
  • How to evaluate a composite function?
  • What happens when a function is composed of itself?
  • How to express a composite function schematically?
  • How to evaluate composite functions from graphs?
  • How to evaluate composite functions from tables?
  • How to find the domain of a composite function?
  • How to find the range of a composite function?

Introduction

Consider a situation in which you have, for example, a function f(x) = xx and another function g(x) = 2x. What happens if you insert the whole expression of g(x) in the place of the variable x in the first function f(x)? What if you insert the whole expression of f(x) in the function g(x)? What is the new function obtained? Is this the same function as that obtained in the previous combination?

In general, the functions discussed so far have been simple functions, in the sense that they were not obtained from the combination of two or more other functions. In fact, if we have dealt with combined functions in some cases, this has gone unnoticed because the focus was elsewhere. Now, we will explain what happens when one function acts as the input of another function.

Please select a specific "Composite Functions" lesson from the table below, review the video tutorial, print the revision notes or use the practice question to improve your knowledge of this math topic.

Functions Learning Material
Tutorial IDMath Tutorial TitleTutorialVideo
Tutorial
Revision
Notes
Revision
Questions
16.4Composite Functions
Lesson IDMath Lesson TitleLessonVideo
Lesson
16.4.1The Meaning of Composite Function
16.4.2Properties of Composite Functions
16.4.3Evaluating Composite Functions
16.4.4Function Composition with Itself
16.4.5Showing a Composite Function Schematically
16.4.6Evaluating Composite Functions from a Graph
16.4.7Evaluating Composite Functions from a Table
16.4.8Domain of a Composite Function
16.4.9Range of a Composite Function

Whats next?

Enjoy the "Composite Functions" math tutorial? People who liked the "Composite Functions" tutorial found the following resources useful:

  1. Math tutorial Feedback. Helps other - Leave a rating for this tutorial (see below)
  2. Functions Revision Notes: Composite Functions. Print the notes so you can revise the key points covered in the math tutorial for Composite Functions
  3. Functions Practice Questions: Composite Functions. Test and improve your knowledge of Composite Functions with example questins and answers
  4. Check your calculations for Functions questions with our excellent Functions calculators which contain full equations and calculations clearly displayed line by line. See the Functions Calculators by iCalculator™ below.
  5. Continuing learning functions - read our next math tutorial: Piecewise Functions

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