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AlgebraIntroduction

Chaining Functions Together

Part of Composite Functions — GCSE Mathematics

This introduction covers Chaining Functions Together within Composite Functions for GCSE Mathematics. Revise Composite Functions in Algebra for GCSE Mathematics with 14 exam-style questions and 12 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 1 of 7 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 7

Practice

14 questions

Recall

12 flashcards

Chaining Functions Together

Imagine you have two machines: Machine G turns any number into double that number, and Machine F adds 3. If you want to double a number AND THEN add 3, you'd run it through G first, then F. This is called a COMPOSITE function - you chain the machines together to create a more complex process.
Composite functions diagram

Keep building this topic

Read this section alongside the surrounding pages in Composite Functions. That gives you the full topic sequence instead of a single isolated revision point.

Key FactsMethod: Finding Composite FunctionsWorked Example 1: Composite Functions with Values

Practice Questions for Composite Functions

The composite function fg(x) means: A) Apply g first, then apply f to the result B) Apply f first, then apply g to the result C) Multiply f(x) by g(x) D) Add f(x) to g(x)

  • A. Apply g first, then apply f to the result
  • B. Apply f first, then apply g to the result
  • C. Multiply f(x) by g(x)
  • D. Add f(x) to g(x)
1 markfoundation

Explain why, in general, fg(x) and gf(x) are NOT equal. You may use an example to support your explanation.

2 marksfoundation

Quick Recall Flashcards

What does fg(x) mean?
fg(x) = f(g(x)): apply g first (inner function), then apply f to the result. Do the function closest to x first.
What is a composite function?
A function formed by chaining two functions together. The output of one function becomes the input of the next.

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