DfE statement A7 · Algebra

Functions, inverse and composite functions

part HigherNon-calculator

Functions, inverse and composite functions is content statement A7 of the DfE GCSE mathematics subject content, in the algebra area. It is on both tiers, with a Higher-only part, and it is examined without a calculator. Below is what the specification actually requires, the 3 mistakes that cost marks on this topic most often, and practice questions written to the statement — original questions, not past papers.

What the specification says

The DfE subject content for GCSE mathematics states, verbatim: "Where appropriate, interpret simple expressions as functions with inputs and outputs; interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’." (statement A7). Every awarding organisation — Pearson Edexcel, AQA and OCR — must cover it, so the wording is the same whichever specification your school follows.
— Department for Education, Mathematics: GCSE subject content and assessment objectives, statement A7

Tier

Both tiers, but part of it is Higher only. Foundation covers the statement except for the following, which the DfE prints in bold and reserves for Higher: "interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’". Everything else in the statement is Foundation content.

Calculator

This is non-calculator territory. Questions on it belong naturally on Paper 1, where written method is all you have — so practise it that way rather than with a calculator to hand.

Common mistakes

Applying fg(x) in the wrong order. fg(x) means do g first, then f.
Confusing the inverse function with the reciprocal: f⁻¹(x) is the function that undoes f, not 1/f(x).
Reading f(x + 2) as f(x) + 2. The first substitutes x + 2 into the function; the second adds 2 to the output.

Sample questions (10 of 30)

A7 · Functions, inverse and composite functionsQuestion 1 of 10 · 0 correct

Practice mode· no pressure · hints available

Algebra

Expert

The function f(x) = x² for all real values of x has no inverse function, but g(x) = x² for x ≥ 0 does have one. Which statement correctly explains this?

y = x²

💡 Hints:

Foundation worksheet Higher worksheet Foundation algebra practice Higher algebra practice

Nearby statements

A5Rearranging formulae A6Identities, equivalence and algebraic proofpart Higher A8Coordinates in all four quadrants A9Straight-line graphs and y = mx + cpart Higher

Questions people ask

Is functions, inverse and composite functions on Foundation or Higher?

Both, but not all of it. The parts the DfE prints in bold — "interpret the reverse process as the ‘inverse function’; interpret the succession of two functions as a ‘composite function’" — are Higher only; the rest is Foundation content.

Can I use a calculator for functions, inverse and composite functions?

Not on Paper 1, which is where this normally appears. Paper 1 is non-calculator for both tiers and carries the same 80 marks as each of the other two papers.

What is the single most common mistake here?

Applying fg(x) in the wrong order. fg(x) means do g first, then f.

Are these past paper questions?

No. Every question is original, written to this DfE content statement and checked before publication. We do not host past papers or mark schemes.

Back to Algebra at Foundation or at Higher.