View source for Domain of a function

In [[mathematics]], and more specifically in [[naive set theory]], the '''domain of definition''' (or simply the '''domain''') of a [[Function (mathematics)|function]] is the set of "input" or [[Argument of a function|argument]] values for which the function is defined.

That is, the function provides an "output" or [[Value (mathematics)|value]] for each member of the domain.

== Description ==

Conversely, the set of values the function takes on as output is termed the image of the function, which is sometimes also referred to as the [[Range (mathematics)|range]] of the function.

For instance, the domain of cosine is the set of all real numbers, while the domain of the square root consists only of numbers greater than or equal to 0 (ignoring complex numbers in both cases). When the domain of a function is a subset of the real numbers, and the function is represented in an xy Cartesian coordinate system, the domain is represented on the x-axis.

== See also ==

* [[Bijection]], [[injection]], and [[surjection]]
* [[Codomain]]
* [[Domain decomposition]]
* [[Effective domain]]
* [[Lipschitz domain]]
* [[Naive set theory]]
* [[Range (mathematics)]]

== External links ==

* [https://en.wikipedia.org/wiki/Domain_of_a_function Domain of a function] @ Wikipedia.org 

[[Category:Mathematics]]
[[Category:Set theory]]