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.