# Domains

The domain of a function is the set of all values for which the function is defined.

For most functions in algebra, the domain is the set of all real numbers.  But, there are two cases where this is not always true, fractions with a variable in the denominator and radicals with an even index.

Example 1:

Find the domain of .

Since division by zero is undefined in the real number system, .  So the domain is all real numbers except 2.

Example 2:

Find the domain of .

Since we can only take the square root of a non-negative number, the domain is all real numbers greater than or equal to 2.

You may sometimes be presented with an equation and a domain of possible solutions. In this case the domain means the set of possible values for the variable.

Example 3:

Solve the equation

over the domain {0, 1, 2, 3}.

This is a tricky equation; it's not linear and it's not quadratic, so we don't have a good method to solve it. However, since the domain only contains four numbers, we can just use trial and error.

So the solution set over the given domain is {0, 1}.