AlgebraDeep Dive

Method: Finding an Inverse Function

Part of Inverse Functions — GCSE Mathematics

This deep dive covers Method: Finding an Inverse Function within Inverse Functions for GCSE Mathematics. Revise Inverse Functions in Algebra for GCSE Mathematics with 8 exam-style questions and 4 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 3 of 6 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 6

Practice

8 questions

Recall

4 flashcards

Method: Finding an Inverse Function

1Write y = f(x)

2Swap x and y

3Rearrange to make y the subject

4Replace y with f⁻¹(x)

Keep building this topic

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

Key Facts Worked Example 1: Finding an Inverse Functions as Machines Worked Example 2: Verifying an Inverse

Practice Questions for Inverse Functions

What does f⁻¹(x) represent?

A. The reciprocal of f(x), i.e. 1/f(x)
B. The function that undoes f(x)
C. The square of f(x)
D. The negative of f(x)

1 markfoundation

Explain why the function f(x) = x² (for all real x) does not have an inverse function over its full domain.

2 markshigher

Quick Recall Flashcards

What is an inverse function?

A function that undoes what the original function does. f⁻¹(x) reverses the operation of f(x)

What does f⁻¹ notation mean?

Inverse function (NOT 1/f). It's the function that undoes f, not the reciprocal

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Key Facts

Worked Example 1: Finding an Inverse