Search results
Results From The WOW.Com Content Network
The function g must equal the inverse of f on the image of f, but may take any values for elements of Y not in the image. A function f with nonempty domain is injective if and only if it has a left inverse. [21] An elementary proof runs as follows: If g is the left inverse of f, and f(x) = f(y), then g(f(x)) = g(f(y)) = x = y.
In mathematics, the domain of a function is the set of inputs accepted by the function. It is sometimes denoted by or , where f is the function. In layman's terms, the domain of a function can generally be thought of as "what x can be". [ 1] More precisely, given a function , the domain of f is X. In modern mathematical language, the domain is ...
In mathematics, a surjective function (also known as surjection, or onto function / ˈɒn.tuː /) is a function f such that, for every element y of the function's codomain, there exists at least one element x in the function's domain such that f(x) = y. In other words, for a function f : X → Y, the codomain Y is the image of the function's ...
Assuming that the domains of the functions are open intervals: A necessary, but not sufficient, condition for a function f to have an antiderivative is that f have the intermediate value property. That is, if [a, b] is a subinterval of the domain of f and y is any real number between f(a) and f(b), then there exists a c between a and b such ...
In mathematical analysis, the Dirac delta function (or δ distribution ), also known as the unit impulse, [ 1] is a generalized function on the real numbers, whose value is zero everywhere except at zero, and whose integral over the entire real line is equal to one. [ 2][ 3][ 4] Since there is no function having this property, modelling the ...
In mathematics, orthogonal functions belong to a function space that is a vector space equipped with a bilinear form. When the function space has an interval as the domain, the bilinear form may be the integral of the product of functions over the interval: The functions and are orthogonal when this integral is zero, i.e. whenever .
In mathematics, an iterated function is a function that is obtained by composing another function with itself two or several times. The process of repeatedly applying the same function is called iteration. In this process, starting from some initial object, the result of applying a given function is fed again into the function as input, and ...
Fixed point (mathematics) A function with three fixed points. In mathematics, a fixed point (sometimes shortened to fixpoint ), also known as an invariant point, is a value that does not change under a given transformation. Specifically, for functions, a fixed point is an element that is mapped to itself by the function.