AlgebraIntroduction

Functions as Machines

Part of Inverse FunctionsGCSE Mathematics

This introduction covers Functions as Machines 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 1 of 6 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.

Topic position

Section 1 of 6

Practice

8 questions

Recall

4 flashcards

Functions as Machines

Think of a function as a machine: you put a number in, it does something, and a different number comes out. An INVERSE function is a machine that UNDOES what the first machine did - it takes the output and gives you back the original input! It's like having an "undo" button for mathematics.
Inverse functions diagram

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.

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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