![]() 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. Some widely used functions are represented by a symbol consisting of several letters (usually two or three, generally an abbreviation of their name). For example, it is common to write sin x instead of sin( x).įunctional notation was first used by Leonhard Euler in 1734. When the symbol denoting the function consists of several characters and no ambiguity may arise, the parentheses of functional notation might be omitted. In this example, the function f takes a real number as input, squares it, then adds 1 to the result, then takes the sine of the result, and returns the final result as the output. For example, the value at 4 of the function that maps x to ( x + 1 ) 2. When the function is not named and is represented by an expression E, the value of the function at, say, x = 4 may be denoted by E| x=4. ![]() The concept of a function was formalized at the end of the 19th century in terms of set theory, and this greatly enlarged the domains of application of the concept.Ī function is most often denoted by letters such as f, g and h, and the value of a function f at an element x of its domain is denoted by f( x) the numerical value resulting from the function evaluation at a particular input value is denoted by replacing x with this value for example, the value of f at x = 4 is denoted by f(4). Historically, the concept was elaborated with the infinitesimal calculus at the end of the 17th century, and, until the 19th century, the functions that were considered were differentiable (that is, they had a high degree of regularity). For example, the position of a planet is a function of time. įunctions were originally the idealization of how a varying quantity depends on another quantity. ![]() The set X is called the domain of the function and the set Y is called the codomain of the function. In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. ![]()
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