Domain of a function

The domain of a function is the set of inputs for which the function is defined. It specifies which values may be supplied to the function.

Function: A rule or relation that assigns each input in its domain exactly one output. A domain is defined relative to the function whose inputs it permits.
Natural domain: The largest real domain on which a given function formula is defined under the usual conventions. It is the domain obtained by excluding inputs that make the formula undefined.
Codomain: The specified set in which a function’s outputs are required to lie. The domain describes allowed inputs, while the codomain describes the designated output set.
Function composition: The construction that applies one function to the output of another. An input to a composition must produce an intermediate value accepted by the next function.
Set: A collection of distinct objects treated as a mathematical object. A function’s domain is a set of permitted inputs.
Division by zero: An undefined operation in ordinary arithmetic and real-number algebra. Denominators exclude inputs that would make them zero.
Range (mathematics): The set of outputs a function actually attains on its domain. The range is produced from domain inputs and need not equal the codomain.
Piecewise function: A function defined by different formulas on different parts of its domain. Its domain is assembled from the regions assigned to its separate formulas.
Input (mathematics): A value supplied to a mathematical function or procedure. Domain membership determines which inputs the function accepts.
Square root: A number that, when squared, yields a specified value; over the reals, nonnegative values have real square roots. A real-valued square root requires its radicand to be nonnegative.

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