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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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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

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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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