Function (mathematics)
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 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

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

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 sin x instead of sin(x).

Functional notation was first used by Leonhard Euler in 1734. 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 " sin " for the sine function, in contrast to italic font for single-letter symbols.

The functional notation is often used colloqually for referring to a function and simultaneously naming its argument, such as in "let f (x) {\displaystyle f(x)} be a function". This is an abuse of notation that is useful for a simpler formulation.
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