Composition

Definition: Composition

The composition of two functions $f:D\to W$ and $g:D^{\prime }\to W^{\prime }$, where $f(D)\subseteq D^{\prime }$, is the function $g\circ f:D\to W^{\prime }$ defined as

$$(g\circ f)(x)\stackrel{\text{def}}{=}g(f(x))\forall x\in D$$