preimage

plural preimages

1. mathematicsFor a given function, the set of all elements of the domain that are mapped into a given subset of the codomain; (formally) given a function ƒ : X → Y and a subset B ⊆ Y, the set ƒ⁻¹(B) = {x ∈ X : ƒ(x) ∈ B}.

   The preimage of #92;#123;4,9#92;#125; under the function f#58;#92;R#92;rightarrow#92;R#58;f(x)#61;x² is the set #92;#123;-3,-2,#43;2,#43;3#92;#125;.

   3 more examples

   1967 [Academic Press], Francois Treves, Topological Vector Spaces, Distributions and Kernels, 2006, Dover, page 22, The preimage of a neighborhood U of 0 in E must be a neighborhood of (0,x), since (0,x) is mapped into 0.

   Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.

   2003, Sergei K. Lando, Alexander K. Zvonkin, Graphs on Surfaces and Their Applications, Springer, page 56

   Loosely speaking, saying that a function f is one-way implies that given y (in the range of f) it is infeasible to find a preimage of y under f.

   2005, Oded Goldreich, Foundations of Cryptography: A Primer, now Publishers, page 24

   Synonyms: inverse image