Composing Functions

To compose two functionsandis to use the result of one function in the other. If andthen to find to composeandwithwithbeing performed first, findthen find

We can write this asorIn general, the composition ofwithwith being performed first is writtenoror simply(this is distinct from the product ofandwrittenor).

You may think ofbeing used as the argument ofso that ifthenthen if

The composition of functions has some important properties.

1. If a functionis the inverse of a functionso thatthenand

2. Composition of functions is associative so thatIf andthenand

We can compose functions graphically.andas shown below,

Then

and

So that