A composite function is a function where the independent variable of one function is substituted by another function. For example, the composite of $f(x)$ and $g(x)$ could be called $h(x),$ written in function notation below. $$\begin{array}{c}h(x)=f(g(x))\end{array}$$ Say, for example, that $f(x)=\sqrt{4x+3}$ and $g(x)=5^x.$ The composite function $h(x)$ would be created by substituting $g(x)$ for $x$ in $f(x).$ In the table below are more examples of composite functions.

$f(x)$	$g(x)$	$h(x)=f(g(x))$
$f(x)=x^4$	$g(x)=x-6$	$h(x)=(x-6{)}^4$
$f(x)=\log (x)$	$g(x)=3x-5$	$h(x)=\ln (3x-5)$
$f(x)=3^x$	$g(x)=\sqrt{x}$	$y=3^{\sqrt{x}}$