![cover image](https://wikiwandv2-19431.kxcdn.com/_next/image?url=https://upload.wikimedia.org/wikipedia/commons/thumb/3/32/ImagePreimageOfElement.png/640px-ImagePreimageOfElement.png&w=640&q=50)
Image (mathematics)
Set of the values of a function / From Wikipedia, the free encyclopedia
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In mathematics, for a function , the image of an input value
is the single output value produced by
when passed
. The preimage of an output value
is the set of input values that produce
.
![](http://upload.wikimedia.org/wikipedia/commons/thumb/3/32/ImagePreimageOfElement.png/640px-ImagePreimageOfElement.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/9/9d/ImagePreimageofaSet.png/640px-ImagePreimageofaSet.png)
![](http://upload.wikimedia.org/wikipedia/commons/thumb/6/64/Codomain2.SVG/640px-Codomain2.SVG.png)
More generally, evaluating at each element of a given subset
of its domain
produces a set, called the "image of
under (or through)
". Similarly, the inverse image (or preimage) of a given subset
of the codomain
is the set of all elements of
that map to a member of
The image of the function is the set of all output values it may produce, that is, the image of
. The preimage of
, that is, the preimage of
under
, always equals
(the domain of
); therefore, the former notion is rarely used.
Image and inverse image may also be defined for general binary relations, not just functions.