Function Composition

Please Login to access more options.

Definition (Function Composition)

Consider the functions $f:A\to B$ and $g:C\to D$. When $B\subseteq C$, then we know for each $a\in A$ that $f(a)\in B\subseteq C$. Since $f(a)\in C$, we can compute the quantity $g(f(a))$. If $B\subseteq C$, then we define the composition of $g$ and $f$ to be the new function $g\circ f : A\to D$ defined by $$(g\circ f)(a) = g(f(a)).$$