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 .
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 .
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 .
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 .