Composition of functions

Let $g:A\to B$ and $f:B\to C$ be functions. The composition of $f$ and $g$ is the function $\boxed{ (f \circ g): A \rightarrow C }$, can also define this for all $a \in A$ as: $$ (f \circ g)(a) = f(g(a)) $$

We only define the composition $f\circ g$ when the codomain of $g$ is equal to the domain of $f$.