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

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Math Expert
Joined: 02 Sep 2009
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For which of the following functions does f(x) = f(1/x), given that x  [#permalink]

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03 Jul 2015, 02:20
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66% (01:55) correct 34% (02:06) wrong based on 662 sessions

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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.

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

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03 Jul 2015, 02:30
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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 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. $$f(x) = |\frac{x+1}{x+2}|$$

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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, 10:28
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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Posts: 7334
Re: For which of the following functions does f(x) = f(1/x), given that x  [#permalink]

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03 Jul 2015, 20:40
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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1) Absolute modulus : http://gmatclub.com/forum/absolute-modulus-a-better-understanding-210849.html#p1622372
2)Combination of similar and dissimilar things : http://gmatclub.com/forum/topic215915.html
3) effects of arithmetic operations : https://gmatclub.com/forum/effects-of-arithmetic-operations-on-fractions-269413.html
4) Base while finding % increase and % decrease : https://gmatclub.com/forum/percentage-increase-decrease-what-should-be-the-denominator-287528.html

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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, 23:22
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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05 Jul 2015, 05:20
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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Posts: 59
Re: For which of the following functions does f(x) = f(1/x), given that x  [#permalink]

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18 Aug 2017, 02:11
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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Re: For which of the following functions does f(x) = f(1/x), given that x  [#permalink]

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06 Oct 2018, 12:26
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Re: For which of the following functions does f(x) = f(1/x), given that x   [#permalink] 06 Oct 2018, 12:26
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# For which of the following functions does f(x) = f(1/x), given that x

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