Image (mathematics)

For the function that maps a Person to their Favorite Food, the image of Gabriela is Apple. The preimage of Apple is the set {Gabriela, Maryam}. The preimage of Fish is the empty set. The image of the subset {Richard, Maryam} is {Rice, Apple}. The preimage of {Rice, Apple} is {Gabriela, Richard, Maryam}.

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 .

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.


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