Functional notation

Function

x \mapsto f (x)

By domain and codomain

$X$	—›	$B$			$B n$	—›	$B$
$X$	—›	$Z$	—›	$X$
$X$	—›	$R$	—›	$X$	$R n$	—›	$X$
$X$	—›	$C$	—›	$X$	$C n$	—›	$X$

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

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