Editing Function (mathematics) (section)

=== Functional notation ===
The functional notation requires that a name is given to the function, which, in the case of a unspecified function is often the letter {{mvar|f}}. Then, the application of the function to an argument is denoted by its name followed by its argument (or, in the case of a multivariate functions, its arguments) enclosed between parentheses, such as in 

<math display="block">f(x), \quad \sin(3),\quad \text{or}\quad f(x^2+1).</math>

The argument between the parentheses may be a [[variable (mathematics)|variable]], often {{mvar|x}}, that represents an arbitrary element of the domain of the function, a specific element of the domain ({{math|3}} in the above example), or an [[expression (mathematics)|expression]] that can be evaluated to an element of the domain (<math>x^2+1</math> in the above example). The use of a unspecified variable between parentheses is useful for defining a function explicitly such as in "let <math>f(x)=\sin(x^2+1)</math>".

When the symbol denoting the function consists of several characters and no ambiguity may arise, the parentheses of functional notation might be omitted. For example, it is common to write {{math|sin ''x''}} instead of {{math|sin(''x'')}}.

Functional notation was first used by [[Leonhard Euler]] in 1734.<ref>{{cite book|first1=Ron|last1=Larson|first2=Bruce H.|last2=Edwards|title=Calculus of a Single Variable|page=19|year=2010|publisher=Cengage Learning|isbn=978-0-538-73552-0}}</ref> Some widely used functions are represented by a symbol consisting of several letters (usually two or three, generally an abbreviation of their name). In this case, a [[roman type]] is customarily used instead, such as "{{math|sin}}" for the [[sine function]], in contrast to italic font for single-letter symbols.

The functional notation is often used colloquially for referring to a function and simultaneously naming its argument, such as in "let <math>f(x)</math> be a function". This is an [[abuse of notation]] that is useful for a simpler formulation.