The domain of a function is all values that an independent variable can take. The domain of a function is all the input values of the function. If the domain of a function is not explicitly restricted, its domain is called the domain of definition, all points for which the function is defined. The domain of definition can also be called the natural domain. On a Cartesian graph, the domain is typically the horizontal axis.
In the function , the domain of definition is or unrestricted, meaning it can take on any value. However, given the real function , the domain of definition is or , since the square root of a negative number is undefined for the set of real numbers.
A function can also have a restricted domain. For example, take the function with the restriction . While negative numbers are defined for the function, they are not in the domain.
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