tranhaianh1405 wrote:
Carcass wrote:
tranhaianh1405 wrote:
Shouldn't what in the square root be greater than 0, and so the answer should be F only?
not quite sure what you meant Sir
I mean for example suppose that B is correct, then plugging in the denominator would be the square root of -9 and that does not make sense because under the root it should be a positive value.
Good question
So
\(\sqrt{-9}\)
\(\sqrt{(9 \times -1)}\)
\(\sqrt{9} \times \sqrt{-1}\)
\(3 \times \sqrt{-1}\) and \(\sqrt{-1}=i\)
so in the end
\(\sqrt{-9}\)
is basically \(3i\)
So we would have \(\frac{0}{3i}\) = correct option because is 0[/quote]
I agree with what
tranhaianh1405 says about the domain of this rational expression; the ETS "Graduate Record Examinations Mathematical Conventions" (google the title...I do not have enough of a post history to include links) state that we are to assume that all numbers used in the test questions are real numbers, and that when the square root symbol is included in an expression, it means the "non negative square root with the domain >= 0:
"1. All numbers used in the test questions are real numbers. In particular, integers and both rational and irrational numbers are to be considered, but imaginary numbers are not. This is the main assumption regarding numbers. Also, all quantities are real numbers, although quantities may involve units of measurement. "
"5. Here are nine examples of other standard symbols with their meanings:
...
Example 5: [sqrt(x)] the nonnegative square root of x, where [x>=0]"
"6. Because all numbers are assumed to be real, some expressions are not defined. Here are three examples:
...
Example 2: If x<0 then [sqrt(x)] is not defined."
"9. Standard function notation is used in the test, as shown in the following three examples.
Example 1: The function g is defined for all [x >= 0] by [g(x) = 2x + sqrt(2)]
Example 2: If the domain of a function f is not given explicitly, it is assumed to be the set of all real numbers x for which f(x) is a real number. "
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With this in mind, it seems that if we are assuming that the given expression is a "real" function, that the domain would be all real x<-1 and x>3.
This means that the only given answer item that falls into the function's domain is "E".