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For which of the following functions does f(x) = f(1/x), given that x ≠ - 2, - 1, 0, or 1?

A. \(f(x) = |\frac{x+1}{x}|\)

B. \(f(x) = |\frac{x+1}{x-1}|\)

C. \(f(x) = |\frac{x-1}{x}|\)

D. \(f(x) = |\frac{x}{x+1}|\)

E. \(f(x) = |\frac{x+1}{x+2}|\)

Kudos for a correct solution.

The CORRECT Option must satisfy the condition f(2) = f(1/2)

So Checking Options:

A. \(f(x) = |\frac{x+1}{x}|\)

i.e. \(f(2) = |\frac{2+1}{2}| = |\frac{3}{2}|\) and \(f(1/2) = |\frac{0.5+1}{0.5}| = |\frac{3}{1}|\)

Since f(2) is NOT equal to f(1/2) Hence the INCORRECT OPTION

B. \(f(x) = |\frac{x+1}{x-1}|\)

i.e. \(f(2) = |\frac{2+1}{2-1}| = 3/1\) and \(f(x) = |\frac{0.5+1}{0.5-1}| = 3/1\)

Since f(2) is equal to f(1/2) Hence the CORRECT OPTION

C. \(f(x) = |\frac{x-1}{x}|\)

D. \(f(x) = |\frac{x}{x+1}|\)

E. \(f(x) = |\frac{x+1}{x+2}|\)

Answer: Option B _________________

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Re: For which of the following functions does f(x) = f(1/x), given that x [#permalink]

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03 Jul 2015, 11:28

Replace X with 1/x in each option .... Ideally new function got should be same as original. This does not happen in any option. How ever in option B , we get reverse signs but as moduls is there it as good as original function

For which of the following functions does f(x) = f(1/x), given that x ≠ - 2, - 1, 0, or 1?

A. \(f(x) = |\frac{x+1}{x}|\)

B. \(f(x) = |\frac{x+1}{x-1}|\)

C. \(f(x) = |\frac{x-1}{x}|\)

D. \(f(x) = |\frac{x}{x+1}|\)

E. \(f(x) = |\frac{x+1}{x+2}|\)

Kudos for a correct solution.

the best way to solve these type of Q is taking some value of x, and that value too the simplest possible.. here we cannot take 1 or 0 as it is given and these values make few choices undefined.. next simple value will be 2.. we check the values with 2 and 1/2.. ans B
_________________

Re: For which of the following functions does f(x) = f(1/x), given that x [#permalink]

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01 Oct 2016, 12:00

Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

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Re: For which of the following functions does f(x) = f(1/x), given that x [#permalink]

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18 Aug 2017, 03:11

Substitute value as 2 in the expression given in problem statement f(2)=f(1/2). From the options LHS=RHS by substituting the values in the available expression we have Option B.

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