funktionsområde

Funktionsområde, in mathematics, is the set of all input values for which a function is defined. This set is commonly referred to as the domain of the function. The funktionsområde is typically denoted Dom(f) or simply the domain. It differs from the codomain (the set that could contain outputs) and from the range (the actual set of outputs produced by the function).

For real-valued functions, the domain is a subset of the real numbers and is often an interval or a union of intervals. Examples illustrate how the domain is determined by the expression defining the function: f(x) = sqrt(x - 1) has domain [1, ∞) because the radicand must be nonnegative; f(x) = 1/x has domain (-∞, 0) ∪ (0, ∞) since division by zero is not allowed; f(x) = ln(x) has domain (0, ∞) because the logarithm requires a positive argument. For functions of two variables, such as f(x, y) = sqrt(x - y^2), the domain is the set of all (x, y) with x ≥ y^2.

When determining the domain, one imposes all restrictions implied by the function’s defining expressions: nonnegative radicands for even roots, nonzero denominators, positive arguments for logarithms, and so on. The domain can be a single interval, a union of intervals, or a more general region in higher dimensions. In graphing contexts, the domain corresponds to the horizontal extent of the graph; in complex analysis, the domain may be a region in the complex plane.