Composition of Functions V2
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?