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Worked Example 1: Finding an Inverse

Part of Inverse Functions — GCSE Mathematics

This study notes covers Worked Example 1: Finding an Inverse 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 4 of 6 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 4 of 6

Practice

8 questions

Recall

4 flashcards

Worked Example 1: Finding an Inverse

f(x) = 3x − 5. Find f⁻¹(x).

Step 1 Write y = 3x − 5

y = 3x − 5

Step 2 Swap x and y

x = 3y − 5

Step 3 Rearrange for y

x + 5 = 3y

y = (x + 5)/3

Step 4 Write the answer

f⁻¹(x) = (x + 5)/3

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.

Method: Finding an Inverse FunctionWorked Example 2: Verifying an InverseFunctions as MachinesKey Facts

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 does f⁻¹ notation mean?
Inverse function (NOT 1/f). It's the function that undoes f, not the reciprocal
What is an inverse function?
A function that undoes what the original function does. f⁻¹(x) reverses the operation of f(x)

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Method: Finding an Inverse Function

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Worked Example 2: Verifying an Inverse