Functions
Notation f(x), composite f(g(x)), inverse f−1(x). Higher tier.
f(x) is the function applied to x. Composite f(g(x)) means ‘do g first, then f’. Inverse f−1(x) reverses f: solve y = f(x) for x.
Worked examples
f(x) = 2x + 3, f(5) = 13.
g(x) = x². f(g(2)) = f(4) = 11.
f(x) = 2x + 3 has inverse f−1(x) = (x − 3)/2.
Frequently asked questions
f(g(x)) vs g(f(x))?
Generally NOT equal. Composition isn't commutative.
How to invert?
y = 2x + 3 ⇒ swap x and y ⇒ x = 2y + 3 ⇒ y = (x − 3)/2.