Composition Order Matters

Function composition is not commutative and is not multiplication: f(g(x)), g(f(x)), and f(x) · g(x) are three different things.

For f(x) = x² and g(x) = x + 1 at 2: f(g(2)) = 9, g(f(2)) = 5, and f(2) · g(2) = 12 — three wirings, three answers.