Function Notation

Mathematics needs a compact, unambiguous way to talk about functions, and that is what function notation provides. The single symbol f(x) packs in the name of the rule, its input, and its output, all at once. Once you are fluent in this shorthand, evaluating, inverting and combining functions becomes clean and quick.

In this lesson you will read and use the notations \(f(x)\) and \(f:x\mapsto\ldots\), evaluate a function at a value, and meet the two operations that build new functions from old: the inverse \(f^{-1}\) and the composite \(fg(x)=f(g(x))\). You will also see what \(f^2(x)\) really means, which is not what many students first guess.