Thank you so much for showing me how to do this one.
GMATPrep PS Function
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 cans
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f(x)=f(1x)?
a) f(1x) = 1 (1x) = x != f(x) incorrect
b) f(1x) = 1  (1x)^2 = 1  (1+x^2  2x) = 2x  x^2 !=f(x) incorrect
c) f(1x) = (1x)^2  (1(1x))^2 = (1x)^2  x^2 = f(x) incorrect
d) f(1x) = (1x)^2 *(1(1x))^2 = (1x)^2 * (x)^2 = f(X) correct
e) f(1x) = (1x)/x = 1/f(x) incorrect
IMO D
a) f(1x) = 1 (1x) = x != f(x) incorrect
b) f(1x) = 1  (1x)^2 = 1  (1+x^2  2x) = 2x  x^2 !=f(x) incorrect
c) f(1x) = (1x)^2  (1(1x))^2 = (1x)^2  x^2 = f(x) incorrect
d) f(1x) = (1x)^2 *(1(1x))^2 = (1x)^2 * (x)^2 = f(X) correct
e) f(1x) = (1x)/x = 1/f(x) incorrect
IMO D
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Cans!!
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Cans!!

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Plug x = 1  x in the options.
(A) f(x) = 1  x, f(1  x) should give the same value i.e. 1  x when x = 1  x
f(1  x) = 1  (1  x) = 1  1 + x = x. Not True.
(B) f(x) = 1  xÂ², f(1  x) = 1  (1  x)Â². Not True.
(C) f(1  x) = (1  x)Â²  [1  (1  x)Â²]. Not True.
(D) f(x) = xÂ²(1  x)Â²; f(1  x) = (1  x)Â² [1  (1  x)]Â² = (1  x)Â²[1  1 + x]Â² = (1  x)Â²(x)Â² = f(x). True.
The correct answer is D.
Anurag Mairal, Ph.D., MBA
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 GMATGuruNY
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Let x=2.For which of the following functions f is f(x) = f(1x) for all x?
a. f(x)= 1x
b. f(x)= 1xÂ²
c. f(x)= xÂ²(1x)Â²
d. f(x)= xÂ²(1x)Â²
e. f(x)= x/(1x)
Then f(x) = f(2) and f(1x) = f(12) = f(1).
The question becomes:
For which of the following functions does f(2) = f(1)?
Answer choice A:
f(2) = 12 = 1.
f(1) = 1(1) = 2.
Doesn't work.
Answer choice B:
f(2) = 1  2Â² = 3.
f(1) = 1  (1)Â² = 0.
Doesn't work.
Answer choice C:
f(2) = 2Â²  (12)Â² = 4  1 = 3.
f(1) = (1)Â²  [1(1)]Â² = 14 = 3.
Doesn't work.
Answer choice D:
f(2) = 2Â² * (12)Â² = 4 * 1 = 4.
f(1) = (1)Â² * [1(1)]Â² = 1 * 4 = 4.
Success!
Answer choice E:
f(2) = 2/(12) = 2.
f(1) = (1)/[(1(1)] = 1/2.
Doesn't work.
The correct answer is D.
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