Codomain of a function


Since you may be dealing with functions and relations unto their depths, knowing better about domain and range sets would be considerable.

Codomain of a function

The codomain of a function is known to be its set of possible outputs. In other words, codomain is a set of elements that may possibly and logically be produced by the function and the inputs that may be entered.

For instance, consider the use of function notation f: R→R, It would certainly mean that f is a function from real number to real number. In other words, it could be said that the codomain of f is a set of real numbers R (also the set of its possible inputs or domains is also supposed to be a set of real numbers RR).

Now, just because an object exists as the codomain of a function, it does not imply that it would come out as an outcome for the inputs entered for the function. Consider an example,

Suppose that we have defined a function f: R→R, $f(x)=x^{2}$. Here, since f(x) would always be non-negative, the number -3 despite being a codomain of the function cannot come out as an outcome since there are no inputs that could actually result in a negative outcome. The set of all outputs that would be received from putting in all inputs into the function is called range. While range is a set of non-negative real numbers, codomain is a set of all considerable real numbers.

It may now be clear to you that a “codomain of a relation or a function is a set of values which include the range as explained earlier and can include additional values apart from the ones in the range.

Codomains are of importance in the following cases:

  • When you are required to restrict the outputs of a considered function. For instance, by specifying a codomain as a “set of positive real numbers”, you may be instructing the ones who’re ignoring any negative values while using the function.
  • It might be difficult to specify the range exactly. However, a larger set of numbers that includes a few that could possibly be the part of the range can surely be specified. For instance, a codomain could define a set of entirely positive real numbers even though; a function does not generate all positive real numbers.

Since the range is quite difficult to be specified, thinking about the codomain could help in attaining the range.


Content Protection by
Please Share