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.
If a functionis the inverse of a functionso thatthenand
Composition of functions is associative so thatIf andthenand
We can compose functions graphically.andas shown below,