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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 ...
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.
Range of a function. is a function from domain X to codomain Y. The yellow oval inside Y is the image of . Sometimes "range" refers to the image and sometimes to the codomain. 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.
t. e. In the study of differential equations, a boundary-value problem is a differential equation subjected to constraints called boundary conditions. [ 1] A solution to a boundary value problem is a solution to the differential equation which also satisfies the boundary conditions. Boundary value problems arise in several branches of physics ...
In mathematical analysis, the maximum and minimum[ a] of a function are, respectively, the largest and smallest value taken by the function. Known generically as extremum, [ b] they may be defined either within a given range (the local or relative extrema) or on the entire domain (the global or absolute extrema) of a function. [ 1][ 2][ 3 ...
The definitions can be generalized to functions and even to sets of functions. Given a function f with domain D and a preordered set (K, ≤) as codomain, an element y of K is an upper bound of f if y ≥ f (x) for each x in D. The upper bound is called sharp if equality holds for at least one value of x. It indicates that the constraint is ...
Look up calculus in Wiktionary, the free dictionary. In mathematics education, calculus is an abbreviation of both infinitesimal calculus and integral calculus, which denotes courses of elementary mathematical analysis. In Latin, the word calculus means “small pebble”, (the diminutive of calx, meaning "stone"), a meaning which still ...
Saddle point. In mathematics, a saddle point or minimax point[ 1] is a point on the surface of the graph of a function where the slopes (derivatives) in orthogonal directions are all zero (a critical point ), but which is not a local extremum of the function. [ 2] An example of a saddle point is when there is a critical point with a relative ...