AlgebraDeep Dive

Finding the Inverse Function

Part of Function Notation · GCSE GCSE Mathematics revision

This deep dive covers Finding the Inverse Function within Function Notation for GCSE Mathematics. Revise Function Notation in Algebra for GCSE Mathematics with 10 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 3 of 5 in this topic. Use this deep dive to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 3 of 5

Practice

10 questions

Recall

3 flashcards

Finding the Inverse Function

1 Write y = f(x)

2 Swap x and y

3 Rearrange to make y the subject

4 Replace y with f⁻¹(x)

Keep building this topic

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

Key Notation Worked Example: Find Inverse Input → Process → Output Knowledge Organiser: Function Notation

Practice Questions for Function Notation

If f(x) = x² − 1, what does f(3) equal?

A. 3
B. 7
C. 8
D. 9

1 markfoundation

f(x) = x + 3 and g(x) = 2x. Show with an example that fg(x) ≠ gf(x), and explain why the order matters.

2 markshigher

Quick Recall Flashcards

Quadratic Sequence

Second differences constant. nth term has n² in it

Inverse Function Method

Write y = f(x), swap x and y, rearrange for y, write as f⁻¹(x)

10 questions on Function Notation — practise free

Instant marking, adaptive difficulty, and 3 spaced repetition flashcards. Free until your GCSEs.

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Key Notation

Worked Example: Find Inverse