Definition 5.32 (Composition of Functions)

For 5.1 Sets $A$, $B$, and $C$,
let $f:A\to B$ and $g:B\to C$ be functions
The $\text{composition}$ of the functions $f$ and $g$, denoted by $g\circ f$, is the function $(g\circ f):A\to C,\text{ given by }(g\circ f)(a):=g(f(a))$

$\text{We read }g\circ f\text{ as }\text{‘}g\text{ of }f\text{’}$