A composite function, or a composition of functions, combines two or more functions, which produces a new function. In a composition, the outputs produced by one function are the inputs of the other function. The composition of the functions $f$ and $g$ is denoted as $f(g(x))$ or $(f\circ g)(x).$ Performing the composition of two functions is similar to evaluating one function into the other. For example, let $f(x)=2x+1$ and $g(x)=x-5.$ To find $f(g(x)),$ the variable $x$ in $f(x)=2x+1$ must be substituted with $g(x).$ Note that $f(g(x))$ makes sense only when the outputs of $g$ belong to the domain of $f.$ Also, be aware that the composition of functions is not commutative — that is, in general, $f(g(x))\ne g(f(x)).$ This can be checked with the same two functions. Just as changing the order of the machines in a factory could alter the final product, changing the order in which the functions are applied could produce different outputs. For example, here $f(g(2))$ and $g(f(2))$ are different values.