In mathematics, the domain and codomain of a function are two distinct concepts that are related to the input and output of the function.
The domain of a function is the set of all possible input values for the function. It represents the set of values for which the function is defined and makes sense. For example, if we have a function f(x) = x^2, the domain of this function is all real numbers, since we can square any real number.
The codomain of a function, on the other hand, is the set of all possible output values for the function. It represents the set of values that the function can potentially produce. For example, for the same function f(x) = x^2, the codomain is also all real numbers, since we can square any real number to get another real number.
Note that the range of a function is a subset of its codomain and represents the set of actual output values that the function produces for the given input values. In some cases, the range may be equal to the codomain, but in other cases, it may be a proper subset.
In summary, the domain of a function is the set of all possible input values, the codomain is the set of all possible output values, and the range is the set of actual output values produced by the function for the given input values.
