# Composite function

If we have two functions $f(x)$ and $g(x)$, we can make a new function by applying $f$ followed by $g$, namely $h(x)=g\bigl(f(x)\bigr)$. Then $h$ is called a composite function, and we write $h=g\circ f$ or $h=gf$.

To be able to do this, we require that the range of $f$ is contained within the domain of $g$.