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# GRE prep Club test question; Question ID Q02-43

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GRE prep Club test question; Question ID Q02-43 [#permalink]  26 Jun 2017, 10:25
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Assume the function $$f(x)=(x−5)^2+ sqrt(x+3) + \frac{5}{(x+2)}$$

For which of the values f(x) is defined?
Indicate all possible values.
a. 6
b. 5
c. 4
d. 3
e. 2
f. 1

i dont understand the explaination

or f(x) to be defined, the individual terms of f(x) need to be real. The conditions are analysed below:

(x−5)^2 will be real regardless any value of x<
√x+3 will be defined if x≥−3 So, D, E , F are possible.
5/(x+2) will be defined if the denominator (x+2)≠0(. So x cannot be -2. So the only options remain are D and F.
[Reveal] Spoiler: OA
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Re: GRE prep Club test question; Question ID Q02-43 [#permalink]  26 Jun 2017, 15:18
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Expert's post
The question had a typo. The last term is $$\frac{5}{x-2}$$.

If any individual term becomes undefined or infinity then the function becomes undefined or infinity.
Since complex number / infinity + real number is complex number or infinity.

So you have to check each term one by one to make sure they comply with the definitions.

Hope you get this!
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Sandy
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Re: GRE prep Club test question; Question ID Q02-43 [#permalink]  26 Jun 2017, 19:45
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BUt all the values fit except for 2..then hoow is the answer d and f only?
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Re: GRE prep Club test question; Question ID Q02-43 [#permalink]  27 Jun 2017, 06:27
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i still dont get it(i feel dumb!).. sqrt(x+3) >=0 for it to be real... so x+3>=0 , hence x>=-3 and all the values in the answer choices are greater than -3; we obviously rule out 2 because the typo u mention... then how is the answer d and f..

Please explain...This question is making me doubt mt sanity!!
GRE Prep Club Legend
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Re: GRE prep Club test question; Question ID Q02-43 [#permalink]  27 Jun 2017, 10:41
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Expert's post
Hi,

I am sorry the answers of question was wrong. You are right all the values greater than equal to 3 except 2 are correct answer.

You had it absolutely right from the start.

I have fixed the question.

Sincerely,
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Sandy
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Re: GRE prep Club test question; Question ID Q02-43 [#permalink]  27 Jun 2017, 11:41
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thank u for giving my sanity back
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Re: GRE prep Club test question; Question ID Q02-43 [#permalink]  11 Apr 2019, 09:58
sandy wrote:
Hi,

I am sorry the answers of question was wrong. You are right all the values greater than equal to 3 except 2 are correct answer.

You had it absolutely right from the start.

I have fixed the question.

Sincerely,

You mean all the values greater than equal to -3 except -2 right?
Re: GRE prep Club test question; Question ID Q02-43   [#permalink] 11 Apr 2019, 09:58
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