SOLUTION: what is the restrictions on a domain of a variable?

Question 125356: what is the restrictions on a domain of a variable?
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
1st The variable cannot take a value which would make the denominator zero.
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2nd The variable cannot take a value which would make the radicand of an
even root expression negative.
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Cheers,
Stan H.

Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
A value is in the domain of a function if and only if the function is defined for that value of the independent variable.

For example:

1. . You can substitute any real number for x and the function will be defined. So the domain is all real numbers.

2. . Here, to be defined in the real number system, x cannot be less than zero, so the domain is all positive real numbers and zero. Using set notation you would say {x | x is real, }. On the other hand, if the function were defined in the complex number system, there would be no restriction on the domain.

3. . A value cannot be in the domain of a function if that value causes any denominator in the function to be zero. Here, 3 or -3 would make the denominator zero, and therefore need to be excluded from the domain which is otherwise all real numbers. In interval notation:

(,) U (,) U (,). The parentheses rather than brackets indicate that the endpoints are not included and the U indicates that you want the union of the three intervals.
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