This key facts covers Key Notation 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 2 of 5 in this topic. Use this key facts to connect the idea to the wider topic before moving on to questions and flashcards.
Key Notation
| Notation | Meaning | Example (if f(x) = 2x + 1) |
|---|---|---|
| f(x) | The function rule | f(x) = 2x + 1 |
| f(3) | Output when input is 3 | f(3) = 2(3) + 1 = 7 |
| f⁻¹(x) | Inverse function | f⁻¹(x) = (x − 1)/2 |
| fg(x) | Composite: f of g(x) | Do g first, then f |
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
Inverse Function Method
Write y = f(x), swap x and y, rearrange for y, write as f⁻¹(x)
Quadratic Sequence
Second differences constant. nth term has n² in it