preimage (plural preimages)

  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\rightarrow \R:f(x)=x^2 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.
    • 2003, Sergei K. Lando, Alexander K. Zvonkin, Graphs on Surfaces and Their Applications, Springer, page 56 ↗,
      Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.
    • 2005, Oded Goldreich, Foundations of Cryptography: A Primer, now Publishers, page 24 ↗,
      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.
  • (set of all elements that map into a given subset of the codomain of a function) inverse image
Related terms Translations
  • German: Urbild
  • Portuguese: pré-imagem

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