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.
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.
Practice questions for Inverse Functions
What does f⁻¹(x) represent?
Explain why the function f(x) = x² (for all real x) does not have an inverse function over its full domain.
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