preimage

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preimage (plural preimages)

(mathematics) The set containing exactly every member of the domain of a function such that the member is mapped by the function onto an element of a given subset of the codomain of the function. Formally, of a subset B of the codomain Y under a function ƒ, the subset of the domain X defined by

$f^{-1}(B) = \{x \in X : f(x) \in B\}.$

For example, the preimage of {4, 9} under the squaring function is the set {−3,−2,+2,+3}.