different between function vs preimage

English

Etymology

From Middle French function, from Old French fonction, from Latin functi? (“performance, execution”), from functus, perfect participle of fungor (“to perform, execute, discharge”).

Pronunciation

• (UK) IPA^(key): /?f??(k)??n/, /?f??k?n?/
• (US) IPA^(key): /?f??k??n/, [?f??k???n], [?f??k?n?]
• Hyphenation: func?tion
• Rhymes: -??k??n

Noun

function (plural functions)

1. What something does or is used for.

   Synonyms: aim, intention, purpose, role, use

2. A professional or official position.

   Synonyms: occupation, office, part, role

4. An official or social occasion.

   Synonyms: affair, occasion, social occasion, social function

5. Something which is dependent on or stems from another thing; a result or concomitant.
6. A relation where one thing is dependent on another for its existence, value, or significance.
7. (mathematics) A relation in which each element of the domain is associated with exactly one element of the codomain.

   Synonyms: map, mapping, mathematical function, operator, transformation

   Hypernym: relation

8. (computing) A routine that receives zero or more arguments and may return a result.

   Synonyms: procedure, routine, subprogram, subroutine, func, funct

9. (biology) The physiological activity of an organ or body part.
10. (chemistry) The characteristic behavior of a chemical compound.
11. (anthropology) The role of a social practice in the continued existence of the group.

Hyponyms

• subfunction

Derived terms

Related terms

Translations

References

• function on Wikipedia.Wikipedia

Verb

function (third-person singular simple present functions, present participle functioning, simple past and past participle functioned)

1. (intransitive) To have a function.

   Synonyms: officiate, serve

2. (intransitive) To carry out a function; to be in action.

   Synonyms: go, operate, run, work

   Antonym: malfunction

Related terms

• functional
• dysfunction, dysfunctional

Translations

Middle French

Noun

function f (plural functions)

1. function (what something's intended use is)

Descendants

• ? English: function
• French: fonction

English

Etymology

pre- +? image.

Pronunciation

• Rhymes: -?m?d?

Noun

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}.
   • 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.

Synonyms

• (set of all elements that map into a given subset of the codomain of a function): inverse image

Hyponyms

• (set of all elements that map into a given subset of the codomain of a function): kernel

Derived terms

• preimage attack

Related terms

• image

Translations

Further reading

• Image (mathematics) on Wikipedia.Wikipedia
• Kernel (linear algebra) on Wikipedia.Wikipedia