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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 f ( x ) = x + 3 x 2 .

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

Example 2:

Find the domain of f ( x ) = x 2 .

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

x 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

x 2 = x

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.

0 2 = 0 = 0 1 2 = 1 = 1 2 2 2 3 2 3

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



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