Functional notation

x \mapsto f (x)

Examples by domain and codomain

$X$	→	$B,$	$B$	→	$X,$	$B n$	→	$B$
$X$	→	$Z,$	$Z$	→	$X$
$X$	→	$R,$	$R$	→	$X,$	$R n$	→	$X$
$X$	→	$C,$	$C$	→	$X,$	$C n$	→	$X$

Classes/properties

Constant · Identity · Linear · Polynomial · Rational · Algebraic · Analytic · Smooth · Continuous · Measurable · Injective · Surjective · Bijective

Constructions

Restriction · Composition · λ · Inverse

Generalizations

Partial · Multivalued · Implicit

Functional notation is the notation for expressing functions as $f(x)$ which was first used by Leonhard Euler in 1734.^[1] In this notation, an inverse function is expressed as $f^{-1}(x)$ .^[2]

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

This article is issued from Wikipedia. The text is licensed under Creative Commons - Attribution - Sharealike. Additional terms may apply for the media files.