## MA101.7 Composition of functions

Also know as function of a function.

Let $f:A \rightarrow B$ and $g:U \rightarrow V$ be two functions such that $R(f) \subseteq D(g) = U$.

Then the function $h:A \rightarrow V$ defined by $h(x) = g(f(x))$ is called the composite of f and g. The function h is often denoted by $g \cdot f$ (read  g and f).

Thus $(g \cdot f)(x) = g(f(x))$.