Domain, Range, Image and Preimage

Ponder...

For , the image of is and the preimage of is .

Definition 2.13 (Domain, Range, Image, Preimage)

Following Definition 2.11, for , we say that is the domain of and is the range (or codomain).

If and , then is called the image of , and is called a preimage of .

Moreover, if then the image of under is

If , then the preimage of under is

Example

For , the image of is , but the preimage of is . Moreover , , and .

The image of the whole domain, , is usually written and called the image of .