# Composition of functions

It is possible to composite functions. If g and h are functions then the composite function can be described by the following equation:

$[g\circ h](x)=g[h(x)]$

Example

Find the composite function between g(x)=2x-4 and h(x)=-4x+3

We plug our h(x) into our the position of x in g(x), simplify, and get the following composite function:

$[g\circ h](x)=2(-4x+3)-4 =-8x+6-4=-8x+2$

It is important to know that

$[g\circ h](x)\; and \; [h\circ g](x)$

does not have to be equal but if they both are equal to just x then they are inverse functions.

## Video lesson

Find $[g\circ h](x)$ and $[h\circ g](x)$ when $g(x)=4x+4/) and \(h=(\frac{x}{4})-1$ and determine if they are inverse functions.