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Functional notation

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Function
$x \mapsto f (x)$
History of the function concept
Types by domain and codomain
$X \to 𝔹$ $𝔹 \to X$ $𝔹 n \to X$ $X \to ℤ$ $ℤ \to X$ $X \to ℝ$ $ℝ \to X$ $ℝ n \to X$ $X \to ℂ$ $ℂ \to X$ $ℂ n \to X$
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.^[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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Elementary mathematics

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