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AlgebraDeep Dive

Finding the Inverse Function

Part of Function Notation — GCSE Mathematics

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 4 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 4

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 NotationWorked Example: Find InverseInput → Process → Output

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)

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Worked Example: Find Inverse