Word.ws English Dictionary

preimage

preimage noun: 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}.

Noun

preimage (plural preimages)

  1. 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 #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;.
    • 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.
    Synonyms:
    inverse image

Examples of preimage in a sentence

  • 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 of preimage

Forms of preimage

pluralpreimages

Origin of preimage

From pre- + image.

Words formed from preimage

Phrases with preimage

Words that rhyme with preimage

Questions about preimage

What does preimage mean?
Preimage means 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}.
How do you use preimage in a sentence?
Previously, maps and hypermaps were constructed as the preimages of a segment joining two of the three critical values.
What part of speech is preimage?
Preimage is a noun.
What is the plural of preimage?
The plural of preimage is preimages.

Words near preimage in the dictionary

  1. preilluminate
  2. preilluminated
  3. preilluminates
  4. preilluminating
  5. preillumination
  6. preimage
  7. preimage attack
  8. preimage attacks
  9. preimages
  10. preimaginal
  11. preimagine

Source and license

Adapted from Wiktionary: preimage (page history and authors). Text available under the Creative Commons Attribution-ShareAlike 4.0 license. Word.ws reformatted the entry and added links. Wiktionary data of 2026-09-02.

Last updated:

Cite this entry: “preimage.” Word.ws, https://word.ws/preimage. Based on Wiktionary, CC BY-SA 4.0.