Domain, Kodomain, and Range: An Overview

In mathematics, particularly in functions and mappings, understanding domain, kodomain, and range is crucial. These concepts define the relationship between different sets in a function.

Domain

The domain of a function is the complete set of possible input values. For any function f(x), the domain represents all the values x for which the function is defined. For example, in the function f(x) = 1/x, the domain excludes x = 0 because division by zero is undefined.

Kodomain

The kodomain of a function is the set of all possible output values. It defines the range of values that the function could potentially produce. The kodomain is defined when a function is established, though it may not always be the same as the range. For instance, if f(x) = x^2, the kodomain could be all non-negative real numbers, though the actual range might be narrower depending on the specific function.

Range

The range of a function is the actual set of output values that the function produces from the given domain. It is a subset of the kodomain. For the function f(x) = x^2, if the domain is all real numbers, the range is all non-negative real numbers, as squaring any real number will always yield a non-negative result.

In summary, understanding these three components—domain, kodomain, and range—helps in analyzing and working with functions in mathematics. Each plays a distinct role in defining the scope and limitations of a function’s behavior.