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.
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.
(