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GCSE Maths: Functions

Use function notation, find composite functions, and calculate inverse functions. Practise it with adaptive questions for AQA, Edexcel, OCR and Eduqas.

AlgebraFoundation & HigherAQA · Edexcel · OCR · Eduqas

What you need to know

The concepts examiners test on functions, and what each one is really asking.

Evaluate functions for given inputs
Find composite functions fg(x) and gf(x)
Find the inverse of a function f⁻¹(x)
Understand that ff⁻¹(x) = x

Where marks get lost

The exam technique that separates a correct method from a correct answer.

  • Applying functions in the wrong order for composites (fg ≠ gf usually)
  • Not replacing EVERY x when substituting
  • Making errors rearranging for the inverse
  • Confusing f⁻¹(x) with 1/f(x) — they are NOT the same

Functions questions students ask

Is Functions on the Foundation paper?

Yes. Functions appears at both Foundation and Higher tier, though Higher papers take it further.

What should I know before starting Functions?

It builds on Substituting values into expressions and Rearranging equations and Linear equations. If those feel shaky, practise them first — Functions questions assume them.

What is the most common mistake in Functions?

Applying functions in the wrong order for composites (fg ≠ gf usually).

Which exam boards cover Functions?

All four we support — AQA, Edexcel, OCR and Eduqas. GCSE Maths subject content is set by the DfE, so the topic is common to every board; what changes is the paper structure and the grade boundaries.