Image (mathematics)

F At a mathematical function is the image or image set or the image area of ​​a subset M of the domain the set of values ​​from the target set Y, on M actually takes f.

For the words of values ​​or range of values ​​to be used often, but are used by other authors to refer to the entire target set Y. So there is likelihood of confusion. In Germany there is clarity in the classroom, it is only the identifier of values ​​( range of values) used in the sense of image set.

Definition

For a function and a subset of is defined as the following set as the image of M under f:

The image of f is then the image of the set of definitions, thus:

Alternative Notations

For the notation.

The English name ( " in " from the English word image) for is also common.

In general, one uses the usual amount notation to represent the image size, in the above example.

Examples

We consider the function with ( integers ).

• Here, various input variables are not necessarily sent to different image sets:

• The total quantity of the image squares of the function:

Properties

It is a function and and are subsets of:

• Is surjective if and only if.
• Is injective, then similarly apply equality.

The statements about union and intersection can be generalized as two treatments on any family of subsets.