A function is like a machine: put a number in, get a number out. f(x) = 2x + 3 means "double the input and add 3". So f(5) = 2(5) + 3 = 13. The inverse function f⁻¹(x) does the opposite - it undoes what f did!
This introduction covers Input → Process → Output within Function Notation for GCSE Mathematics. Revise Function Notation in Algebra for GCSE Mathematics with 10 exam-style questions and 3 flashcards. This topic appears regularly enough that it should still be part of a steady revision cycle. It is section 1 of 5 in this topic. Use this introduction to connect the idea to the wider topic before moving on to questions and flashcards.
Practice questions for Function Notation
If f(x) = x² − 1, what does f(3) equal?
f(x) = x + 3 and g(x) = 2x. Show with an example that fg(x) ≠ gf(x), and explain why the order matters.
Quick recall flashcards
Quadratic Sequence
Second differences constant. nth term has n² in it
Inverse Function Method
Write y = f(x), swap x and y, rearrange for y, write as f⁻¹(x)