Suppose $f:A\to B$ is defined by $y=f(x)$ and $g:B\to C$ is defined by $z=g(y)$, then $z=g(f(x))=g\circ f(x)$, where $g\circ f:A\to C$ is the composition of $g$ and $f$. To calculate $g\circ f(x)$, we start with $x$ and calculate $f(x)$, then calculate $g(f(x))$; so we start from the inside and work outwards. (In some books these are called compound functions.)

In the context of this course, we often take $A=B={\mathbb{R}}$.