AlgebraKey Facts

Key Facts

Part of Composite FunctionsGCSE Mathematics

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 7 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 7

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.

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