The domain of a function is the set of all $x\text{-}$values, or inputs, for which the function is defined. For example, consider the following functions. Their domains can be written by analyzing the definition of each function.

Function	Analysis	Domain
$f(x)=3x$	Multiplication by $3$ is defined for all real numbers.	All real numbers
$g(x)=\sqrt{x}$	Square roots are not defined for negative numbers.	All non-negative numbers — that is, $x\ge 0$
$h(x)=\frac{1}{x}$	Division by zero is undefined.	All real numbers except $0$ — that is, $x\ne 0$

Depending on how a function is represented, its domain can be determined by using different methods. The domain of a function also depends on what the function describes. For example, let $p(x)=2x$ be a function representing the price of $x$ apples at a market. Although the function is defined for all real numbers, it does not make sense to find the price of a negative number of apples or a fraction of an apple. Here, the domain of $p(x)$ is all non-negative integers.