# Composition of Functions V2

- Author:
- Carlos

Given two functions and , the composition of the functions exists if the target of is a subset of the domain of . Conversely, exists if the target of is a subset of the domain of .
Taking by example the functions and , does the composition exist? What about ?
The two functions are graphed below, evaluate , , . Can you write a general expression for ? what about ?

It is not always possible to compose functions because their domains and targets may not match correctly. The next graph shows and .
Which composition exists without any changes? Which composition has to have the domain/target modified? What changes are necessary?

Examine the next two graphs, and ; and . Is there any intersection between the functions?

Can you make any conjectures about the composition of functions from your observations?