Function Domain

The function domain is the set of elements that contain the independent variable x in any function y = f(x). It is all possible numbers that can be used for the x variable. The domain is established by the nature of the function itself. The domain of a function can also be constricted by definition. The domain for a mathematic equation must unambiguously describe a set of elements that is either finite or infinite. If the domain is not expressly defined or restricted within a mathematic function then it is presumed to be the entire set of real numbers. An example of a domain inherently restricted by the nature of the equation is f(x) = square root of x. Here the square root of a negative number does not exist, so the equation itself limits the domain of x to zero and the positive numbers. The domain of a function can be finite or infinite.

Defined domains:
If the function is y = f(x),
a definition for the domain could be one of the following,
for all x where x is an integer between 0 and 10,
for all x where x > 2,
for all x where x = 12.

Inferred domains:
If y = f(x) is y = x + 1,
y equals x plus one,
then the domain of x is the set of real numbers.

If y = f(x) is y = square root of x,
then the domain is x >= 0.