Domain of a function
In layman's terms, the domain of a function can generally be thought of as "what x can be".In modern mathematical language, the domain is part of the definition of a function rather than a property of it.In the special case that X and Y are both sets of real numbers, the function f can be graphed in the Cartesian coordinate system.The set of specific outputs the function assigns to elements of X is called its range or image.The image of f is a subset of Y, shown as the yellow oval in the accompanying diagram.If a real function f is given by a formula, it may be not defined for some values of the variable.The two concepts are sometimes conflated as in, for example, the study of partial differential equations: in that case, a domain is the open connected subset ofFor example, it is sometimes convenient in set theory to permit the domain of a function to be a proper class X, in which case there is formally no such thing as a triple (X, Y, G).
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