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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 ...
A sigmoid function is any mathematical function whose graph has a characteristic S-shaped or sigmoid curve. A common example of a sigmoid function is the logistic function shown in the first figure and defined by the formula: [1] Other standard sigmoid functions are given in the Examples section. In some fields, most notably in the context of ...
t. e. 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.
A surjective function is a function whose image is equal to its codomain. Equivalently, a function with domain and codomain is surjective if for every in there exists at least one in with . 1 Surjections are sometimes denoted by a two-headed rightwards arrow (U+ 21A0↠RIGHTWARDS TWO HEADED ARROW), 5 as in .
In mathematics, the range of a function may refer to either of two closely related concepts: the codomain of the function, or. the image of the function. In some cases the codomain and the image of a function are the same set; such a function is called surjective or onto. For any non-surjective function the codomain and the image are different ...
e. In mathematics, the logarithm to base b is the inverse function of exponentiation with base b. That means that the logarithm of a number x to the base b is the exponent to which b must be raised to produce x. For example, since 1000 = 103, the logarithm base of 1000 is 3, or log10 (1000) = 3.
Kernel (linear algebra) In mathematics, the kernel of a linear map, also known as the null space or nullspace, is the part of the domain which is mapped to the zero vector of the co-domain; the kernel is always a linear subspace of the domain. [1] That is, given a linear map L : V → W between two vector spaces V and W, the kernel of L is the ...
e. In mathematics, the limit of a function is a fundamental concept in calculus and analysis concerning the behavior of that function near a particular input which may or may not be in the domain of the function. Formal definitions, first devised in the early 19th century, are given below.