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Joined: 29 Aug 2010
Posts: 9

If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim
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Updated on: 30 Oct 2017, 00:43
Question Stats:
58% (01:49) correct 42% (01:53) wrong based on 148 sessions
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If \(f(x)=\frac{1}{x}\) and \(g(x) = \frac{x}{(x^2+1)}\), for all \(x > 0\), what is the minimum value of \(f(g(x))\)? (A) 0 (B) \(\frac{1}{2}\) (C) 1 (D)\(\frac{3}{2}\) (E) 2
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Originally posted by shibbirahamed on 30 Oct 2017, 00:19.
Last edited by Bunuel on 30 Oct 2017, 00:43, edited 1 time in total.
Renamed the topic, edited the question and added the OA.




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Joined: 15 Feb 2017
Posts: 76

If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim
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30 Oct 2017, 03:11
IMO Option E f(g(x)) = \(\frac{x^{2} +1}{x}\) =x + \(\frac{1}{x}\) =(\(\sqrt{x}\) \(\frac{{1}}{{\sqrt{x}}}\))^2+2 The value squared is zero. So the minimum value of the expression is 2. Please give me kudos. I need them badly to unlock gmatclub tests




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Joined: 07 Oct 2018
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Re: If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim
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09 Aug 2019, 07:12
Can someone explain with process how can e) be the ans. when I substituted all the values in x+1/x. I got ans C). Even after using derivation method I got C) as answer not E). What am I missing here?



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Joined: 18 Aug 2017
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Re: If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim
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08 Nov 2017, 14:20
i got 1/2 as answer.. can someone explain?



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Joined: 24 Jun 2017
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Re: If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim
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08 Nov 2017, 16:58
it's not a gmat type question first of all second the solution of user siva is mathematically wrong, you cannot divide by 0 and you can't have 0 under the root. I'm not sure if it can serve as shortcut or it's just a coincidence. There is no way in the real number system that root of x can become 0, but you can assume that there is some x when (√x 1/√x)^2 can take 0 Normally the question should say that x>0 and integer.
answer is indeed 2 because if you think about it x + 1/x and x > 0 (it can be a decimal as well as per problem description) basically when x is minimum (0,00000000.......1) so lim x > +0 then x + 1/x has no solution as 1/0 is undefined.
And if you can just pick up the next integer 1 then x + 1/x so 1+ 1 = 2 check one more 2 > 2 + 1/2 = 2,5 check x=1/2 > 1/2 + 1/(1/2) = still 2,5
looking forward to checking other solutions




Re: If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim
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08 Nov 2017, 16:58






