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 \(g\).