Function Composition

Definition

Given functions \(g : B \to C\) and \(f : A \to B\) we define the composition operation \(\circ\) such that

\[ (g \circ f)(x) = g(f(x)).\]

In particular, we require \(\mathrm{codomain}(f) = \mathrm{domain}(g)\) in order for this to be well defined.