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Domains

Thedomainof afunctionis the set of all values for which the function is defined.

对于大多数函数代数,域是set of allreal 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 thesquare rootof 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 notlinearand it's notquadratic, 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 thesolution setover the given domain is { 0 , 1 } .