# Image (mathematics)

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More generally, evaluating a given function ${\displaystyle f}$ at each element of a given subset ${\displaystyle A}$ of its domain produces a set, called the "image of ${\displaystyle A}$ under (or through) ${\displaystyle f}$". Similarly, the inverse image (or preimage) of a given subset ${\displaystyle B}$ of the codomain of ${\displaystyle f,}$ is the set of all elements of the domain that map to the members of ${\displaystyle B.}$