Composition
The combination of two functions to create a new function.
Definition
Given functions \(f: A \to B\) and \(g: B \to C\), the composition \(g \circ f: A \to C\) is defined by:
\[(g \circ f)(x) = g(f(x))\]
Properties
- Composition is associative: \((h \circ g) \circ f = h \circ (g \circ f)\)
- Composition is not commutative: \(g \circ f \neq f \circ g\) in general