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Function problem

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by leugene » Wed Aug 20, 2008 2:40 pm
It has to be D, I believe.

Don't take my word on this (I'm no math guru), but you might as well plug in numbers for this one. I don't believe you can have a square root of a negative number. Therefore, by plugging into x various numbers you can think of, you want to make sure the resulting sum under the square root is not negative.

It seems that the only answer choice for x that wouldn't result in a negative sum (under the square root) would be 2. And since x is a possible number in your domain, 2 is your answer (domain in this case means a value of x, i believe).

I hope this helps, and if I am wrong, then please correct me.
Last edited by leugene on Wed Aug 20, 2008 2:42 pm, edited 1 time in total.
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by leugene » Wed Aug 20, 2008 2:41 pm
Oh, and it can't be E because then the result on the denominator is zero, and you can't have that.
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by Ian Stewart » Wed Aug 20, 2008 4:57 pm
Nice explanation, leugene- yes, the answer should be D.
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by pepeprepa » Thu Aug 21, 2008 1:35 am
That's long compared to what the question requires but it will perhaps explain it to you more concretely.

You need what is in the square root to be 0 or positive.
If you take x=2 or x<2 it is ok because numerator and denumerator are negative so it gives you a positive result.
If we want both numerator and denumerator to be positive, we need x to be at least equal to 8 (7 is impossible given x-7 at the denumerator).
So you can draw this line:
-------------2--------------7-----8---------------

x must be: x<=2 and x>=8
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by Ian Stewart » Thu Aug 21, 2008 4:48 am
pepeprepa wrote:That's long compared to what the question requires but it will perhaps explain it to you more concretely.

You need what is in the square root to be 0 or positive.
If you take x=2 or x<2 it is ok because numerator and denumerator are negative so it gives you a positive result.
If we want both numerator and denumerator to be positive, we need x to be at least equal to 8 (7 is impossible given x-7 at the denumerator).
So you can draw this line:
-------------2--------------7-----8---------------

x must be: x<=2 and x>=8
Pepeprepa- I think you're answering a different question from what's intended (or at least that's what I'm guessing, based on the answer choices). You are assuming that (x-7) is under the square root, and I'm quite sure it's not supposed to be. That is, you're assuming the function is:

f(x) = root[(x-2)/(x-7)]

whereas the function is presumably supposed to be

f(x) = [root(x-2)]/(x-7)

Otherwise there would be more than one correct answer. You've also assumed (when you say x is at least 8) that x is an integer- not something you can assume here!
For online GMAT math tutoring, or to buy my higher-level Quant books and problem sets, contact me at ianstewartgmat at gmail.com

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by pepeprepa » Thu Aug 21, 2008 4:58 am
You are right, I didn't check well the different possible answers, I would have seen it...
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by vishubn » Thu Aug 21, 2008 10:03 am
hi Ian

I understood the discussion , but i would like to know wat exactly he word " Domain" means in context of value F(x) given here ??

I just didnt get that part :

Vishu
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by Stuart@KaplanGMAT » Thu Aug 21, 2008 1:30 pm
vishubn wrote:hi Ian

I understood the discussion , but i would like to know wat exactly he word " Domain" means in context of value F(x) given here ??

I just didnt get that part :

Vishu
The domain of a function of x (i.e. f(x)) is all the possible values of x.

On most GMAT questions, the domain is specified in the question itself. For example:
For all positive integers x, f(x) = 3(rootx) + 6
has a domain of all positive integers.

"In the domain of the function" just means a possible value for x. So the question could have read,
If F(x)= root(x-2)/(x-7), which of the following is a possible value of x?
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by pre-gmat » Thu Aug 21, 2008 1:55 pm
That's very good explanation. I understand Domain now much better.
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