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For which of the following functions does f(x) = f(1/x), given that x

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

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New post 03 Jul 2015, 03:20
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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. \(f(x) = |\frac{x+1}{x+2}|\)


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

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New post 03 Jul 2015, 03:30
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Bunuel wrote:
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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New post 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

'Hence answer is 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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New post 03 Jul 2015, 21:40
1
Bunuel wrote:
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
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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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New post 04 Jul 2015, 00:22
i think the answer is B

Say x = 4
F(4) = | (4+1)/(4-1)| = 5/3

F(1/4) = |(1/4+1)/(1/4-1)|
= |(5/4)/(-3/4)|
= |(-5/3)|
= 5/3

Can someone show me a faster way to do this question please, other than trial and error?
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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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New post 05 Jul 2015, 06:20
Bunuel wrote:
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.


Correct answer is B.

Substituting x with 1/x in all the expressions we see that only B provides f(x) =f(1/x) and is thus the correct answer.
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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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New post 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.
Re: For which of the following functions does f(x) = f(1/x), given that x   [#permalink] 18 Aug 2017, 03:11
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