Codomain ( $Y in f : X \to Y$ )

The codomain of a function is its specified target set. The image of a function is a subset of the codomain, and equals it precisely for a surjective function. Changing a codomain can change whether the same input-output rule is surjective, as the quadratic function examples under function show.

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In mathematics, particularly in the field of set theory and functions, the **codomain** refers to the set of all possible outputs of a function.

Vs: image: the codomain is the set that the function might reach.

The image is the exact set that it actually reaches.

E.g. the function:

f (x) = x^{2}

could have:

Note that the definition of the codomain is somewhat arbitrary, e.g.

x^{2}

could as well technically have codomain:

R ⋃ R^{2}

even though it will obviously never reach any value in

R^{2}

The exact image is in general therefore harder to characterize.