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The domain of a function is the set of all x-values, called inputs, for which the function is defined. As an example, consider the following functions. f(x) & = 3x [0.2cm] g(x) & = sqrt(x) [0.3em] h(x) & = 1/x Their domains can be written by analyzing the definition of each function.
| Function | Analysis | Domain |
|---|---|---|
| f(x) = 3x | Multiplying 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≥ 0 |
| h(x) = 1/x | Dividing by zero is undefined. | All real numbers except 0 — that is, x≠ 0 |
The domain of a function can be determined through a variety of methods depending on how the function is represented.
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 mangos 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 mangos or a fraction of a mango. Here, the domain of p(x) is all non-negative integers.