AlgebraKey Facts

Key Facts

Part of Composite Functions · GCSE GCSE Mathematics revision

This key facts covers Key Facts 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 2 of 8 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 2 of 8

Practice

14 questions

Recall

12 flashcards

Key Facts

Concept Meaning Example
fg(x) f of g(x) - do g first, then f Apply g, then apply f to result
gf(x) g of f(x) - do f first, then g Apply f, then apply g to result
ff(x) f of f(x) - apply f twice Do f, then do f again
Order matters fg(x) ≠ gf(x) usually Different order = different result

Key insight: fg(x) ≠ gf(x) in general! Order matters!

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.

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 is a composite function?
A function formed by chaining two functions together. The output of one function becomes the input of the next.
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.

14 questions on Composite Functions — practise free

Instant marking, adaptive difficulty, and 12 spaced repetition flashcards. Free until your GCSEs.

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