preimage

Etymology

pre- + image.

noun

1. (mathematics) For 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 4,9 under the function f: R → R :f(x)=x² is the set -3,-2,+2,+3.
   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