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Image (mathematics) - Wikipedia
Image (mathematics)
In mathematics, the image of a function is the set of all such that belongs to the domain of . The image by of an element of the domain of is , that is, the output corresponding to the input . The image by of a subset of the domain of is the set of all such that is in , that is, the set of the images of the elements of . Equivalently, it is the image of the restriction of to .
Preimages or inverse images are defined similarly, by exchanging the roles of the domain and the codomain:
The preimage of an element of the codomain of is the set of all elements of the domain of such that ; it is empty if does not belong to the image of . The preimage of a subset of the codomain of is the set of all elements of the domain of such that . The preimage of the codomain of is, by definition of a function, the domain of .
Images and inverse images may also be defined similarly for general binary relations. in this generalization, images and preimages play symmetric roles: the images and the preimages of a relation are respectively the preimages and the images of the opposite relation.
Printed 2026-06-28.
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