Domääni

Domääni is the Estonian mathematical term for the domain of a function or relation. It denotes the set of input values for which the expression is defined. For a function f: D → Y, D is its domääni; the codomain is Y, and the range is the subset of Y actually reached by f.

Examples help illustrate the concept. For f(x) = sqrt(x − 1), the domääni is { x ∈ R | x ≥ 1 }. For g(x) = 1/x, the domääni is { x ∈ R | x ≠ 0 }. For a function of two variables, f(x, y) = ln(x) + y, the domääni is { (x, y) ∈ R^2 | x > 0 }.

In complex analysis, a function’s domääni is a connected open subset of the complex plane where the function is defined. The domääni is conceptually distinct from the codomain, which is the set of possible outputs, and from the range, which is the actual set of outputs produced by the function.

Determining the domääni involves identifying restrictions that come from the expression itself: avoiding division by zero, ensuring nonnegative radicands in real-valued square roots, and requiring positive arguments for logarithms. In multivariable contexts, the domääni is a subset of a higher-dimensional space, such as R^n or C, defined by the relevant inequalities or equations.

The term is standard in Estonian mathematics education and literature for describing where a function is valid and well-defined.