# Domain (mathematics)

In mathematics, the **domain** of a function is the set of all input values to the function.

Given a function , the set *A* is called the **domain**, or **domain of definition** of *f*.

The set of all values in the codomain that *f* maps to is called the range of *f*, or *f*(*A*).

A well-defined function must map every element of the domain to an element of its codomain. So, for example, the function:

*f*(0). It is thus not a function on the set

**R**of real numbers;

**R**can't be its domain. It is usually either defined as a function on

**R**\\ {0}, or the "gap" is plugged by specifically defining

*f*(0); for example:

*g*to

*S*is written: