FUN019 · Functions & graphs · Classes 11–12
Composite functions
A composite function feeds the output of one function into another. (g ∘ f)(x) = g(f(x)): first f, then g. Order matters.
g ∘ fComposite functions
📐 Formula
f(x) = x + a, g(x) = x²: g(f(x)) = (x + a)², f(g(x)) = x² + a
✏️ Worked example
a = 1, x = 2: f(2) = 3, then g(3) = 9; but f(g(2)) = 4 + 1 = 5.
🌍 Where it is used
Chains of processes: price after tax after discount.
❓ Quick check
f(x) = 2x, g(x) = x + 1. g(f(3)) = ?
🏋️ Practice
EasySame f, g: f(g(3)) = ?
Answer: 8
Mediumf(x) = x², g(x) = x − 2. g(f(x)) = ?
Answer: x² − 2
ChallengeIs f(g(x)) always equal to g(f(x))?
Answer: No