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In mathematics, a function from a set X to a set Y assigns to each element of X exactly one element of Y. [1] The set X is called the domain of the function [2] and the set Y is called the codomain of the function. [3] Functions were originally the idealization of how a varying quantity depends on another quantity.
In mathematics, some functions or groups of functions are important enough to deserve their own names. This is a listing of articles which explain some of these functions in more detail. There is a large theory of special functions which developed out of statistics and mathematical physics.
In mathematics, functions can be identified according to the properties they have. These properties describe the functions' behaviour under certain conditions. A parabola is a specific type of function.
In mathematics, an elementary function is a function of a single variable (typically real or complex) that is defined as taking sums, products, roots and compositions of finitely many polynomial, rational, trigonometric, hyperbolic, and exponential functions, and their inverses (e.g., arcsin, log, or x 1/n).
A function f from X to Y. The set of points in the red oval X is the domain of f. Graph of the real-valued square root function, f(x) = √ x, whose domain consists of all nonnegative real numbers. In mathematics, the domain of a function is the set of inputs accepted by the function.
At the same time, the mapping of a function to the value of the function at a point is a functional; here, is a parameter. Provided that f {\displaystyle f} is a linear function from a vector space to the underlying scalar field, the above linear maps are dual to each other, and in functional analysis both are called linear functionals .
Many special functions appear as solutions of differential equations or integrals of elementary functions.Therefore, tables of integrals [1] usually include descriptions of special functions, and tables of special functions [2] include most important integrals; at least, the integral representation of special functions.
In mathematics, an argument of a function is a value provided to obtain the function's result. It is also called an independent variable. [1]For example, the binary function (,) = + has two arguments, and , in an ordered pair (,).
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