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Revision as of 22:22, 30 August 2013 editWcherowi (talk \| contribs)Extended confirmed users13,260 edits Proposing article for deletion per WP:PROD. (TW)← Previous edit		Revision as of 14:24, 1 September 2013 edit undoColonel Warden (talk \| contribs)Autopatrolled, Extended confirmed users, File movers, Pending changes reviewers, Rollbackers31,041 edits Rewrite, removing prodNext edit →
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			{{Functions}}
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			'''Functional notation''' is the ] for expressing ]s as <math>f(x)</math> which was first used by ] in 1734.<ref>{{citation \|page=19 \|title=Calculus of a Single Variable \|author=Ron Larson, Bruce H. Edwards \|publisher=Cengage Learning \|year=2010 \|isbn=9780538735520}}</ref> In this notation, an ] is expressed as <math>f^{-1} (x)</math>.<ref>{{citation \|title=A Dictionary of Science, Literature and Art \|author=W.T. Brande \|url=http://books.google.com/books?id=yo4DAAAAQAAJ&pg=PA683 \|page=683}}</ref>
	\|concern = Possible copyright violation. This is just cut-and-pasted from the reference.

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			==References==
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	In '''functional notation''', a ], as a ], is combined with another which is regarded as a symbol of ]. Thus <math>f(x)</math> denotes the ] of the performance of the operation <math>f</math> upon the ] <math>x</math>.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref> If upon this result the same operation were repeated, the new result would be expressed by <math>f</math>, or more concisely by <math>f^2(x)</math>, and so on. The quantity <math>x</math> itself regarded as the result of the same operation <math>f</math> upon some other function; the proper symbol for which is, by analogy, <math>f^{-1} (x)</math>.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref> Thus <math>f</math> and <math>f^{-1}</math> are symbols of ]s, the former cancelling the effect of the latter on the subject <math>x</math>. <math>f(x)</math> and <math>f^{-1} (x)</math> in a similar manner are termed ]s.<ref>A dictionary of science, literature and art, ed. by W.T. Brande. Pg </ref>

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Revision as of 14:24, 1 September 2013

Function
x ↦ f (x)
History of the function concept
Types by domain and codomain
`X` → 𝔹 𝔹 → `X` 𝔹 → `X` `X` → ℤ ℤ → `X` `X` → ℝ ℝ → `X` ℝ → `X` `X` → ℂ ℂ → `X` ℂ → `X`
Classes/properties
Constant Identity Linear Polynomial Rational Algebraic Analytic Smooth Continuous Measurable Injective Surjective Bijective
Constructions
Restriction Composition λ Inverse
Generalizations
Relation (Binary relation) Set-valued Multivalued Partial Implicit Space Higher-order Morphism Functor
List of specific functions
v t e

Functional notation is the notation for expressing functions as $f(x)$ which was first used by Leonhard Euler in 1734. In this notation, an inverse function is expressed as $f^{-1}(x)$ .

References

Ron Larson, Bruce H. Edwards (2010), Calculus of a Single Variable, Cengage Learning, p. 19, ISBN 9780538735520
W.T. Brande, A Dictionary of Science, Literature and Art, p. 683

References