Functions as Machines

Part of Inverse Functions · Section 1 of 7

IntroductionUnit: AlgebraGCSE

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 7 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and 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

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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