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 x then they are inverse functions.


Video lesson

Find [g o h](x) and [h o g](x) when g(x)=4x+4 and h=(x/4)-1 and determine if they are inverse functions.