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If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim

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Intern
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B
Joined: 29 Aug 2010
Posts: 15

Kudos [?]: 12 [0], given: 124

If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim [#permalink]

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New post 30 Oct 2017, 00:19
00:00
A
B
C
D
E

Difficulty:

  55% (hard)

Question Stats:

49% (05:00) correct 51% (00:59) wrong based on 86 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
[Reveal] Spoiler: OA

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.

Kudos [?]: 12 [0], given: 124

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Joined: 15 Feb 2017
Posts: 71

Kudos [?]: 58 [4], given: 0

If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim [#permalink]

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New post 30 Oct 2017, 03:11
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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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Re: If f(x) = 1/x and g(x) = x/(x^2 + 1), for all x > 0, what is the minim [#permalink]

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New post 08 Nov 2017, 14:20
i got 1/2 as answer.. can someone explain?

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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 [#permalink]

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New post 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

Kudos [?]: 14 [0], given: 126

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

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