### Images and preimages

Given a function , and — a subset of domain, then the set of all possible values given by on arguments from , we call the image under as is denoted as . So:

Given a subset of the set of values , the sets of all arguments such that their values are in , is called the preimage of under and we denote it as . So:

### Examples

Let , . Then is the set of all even numbers. If is the set of even numbers, then is the set of all natural numbers divisible by . If is the set of odd numbers, then . On the other hand, is the set of even numbers.

Let now , . Then . On the other hand, , and .

Let now , . Then . And .

Let finally , . Therefore, , so it is the line . On the other hand, .