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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.
A function is often denoted by a letter such as f, g or h. The value of a function f at an element x of its domain (that is, the element of the codomain that is associated with x) is denoted by f(x); for example, the value of f at x = 4 is denoted by f(4).
In some cases, when, for a given function f, the equation g ∘ g = f has a unique solution g, that function can be defined as the functional square root of f, then written as g = f 1/2. More generally, when g n = f has a unique solution for some natural number n > 0, then f m/n can be defined as g m.
This is an example of a non-linear functional. The Riemann integral is a linear functional on the vector space of functions defined on [ a , b ] that are Riemann-integrable from a to b . In mathematics , a functional is a certain type of function .
The function g : Y → X is said to be a right inverse of the function f : X → Y if f(g(y)) = y for every y in Y (g can be undone by f). In other words, g is a right inverse of f if the composition f o g of g and f in that order is the identity function on the domain Y of g.
In mathematics, a partial function f from a set X to a set Y is a function from a subset S of X (possibly the whole X itself) to Y. The subset S, that is, the domain of f viewed as a function, is called the domain of definition or natural domain of f. If S equals X, that is, if f is defined on every element in X, then f is said to be a total ...
The intersection of the graph of f with a layer identifies a set of intervals in the domain of f, which, taken together, is defined to be the preimage of the lower bound of that layer, under the simple function. In this way, the partitioning of the range of f implies a partitioning of its domain. The integral of a simple function is found by ...
The domain of f is the set of complex numbers such that (). Every rational function can be naturally extended to a function whose domain and range are the whole Riemann sphere (complex projective line). Rational functions are representative examples of meromorphic functions. [6]