This study notes covers Worked Example: Find Inverse 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 4 of 5 in this topic. Use this study notes to connect the idea to the wider topic before moving on to questions and flashcards.
Worked Example: Find Inverse
f(x) = 3x − 5. Find f⁻¹(x)
Solution
y = 3x − 5
Swap: x = 3y − 5
x + 5 = 3y
y = (x + 5)/3
f⁻¹(x) = (x + 5)/3
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