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

Question

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}|

GMATinsight · Accepted Answer

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

adityadon · Answer

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

chetan2u · Answer

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

whitehalo · Answer

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?

ENGRTOMBA2018 · Answer

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.

FB2017 · Answer

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.

bumpbot · Answer

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

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GMAT Problem Solving (PS) Questions

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

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