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# GMATprep PS question

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Intern
Joined: 07 Nov 2003
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GMATprep PS question [#permalink]  13 May 2006, 23:39
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Question Stats:

0% (00:00) correct 0% (00:00) wrong based on 0 sessions
Guys,
I got this question which i can't figure out, how to go about solving it. what is the question really asking??

For which of the following functions f is f(x) = f(1-x) for all x?
a. f(x) = 1-x
b. f(x) = 1-x^2
c. f(x) = x^2-(1-x)^2
d. f(x) = x^2(1-x)^2
e. f(x) = x/(1-x)

Director
Joined: 08 Jun 2004
Posts: 505
Location: Europe
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D it is.

From the question stem f(x) = f(1-x)

So try to substitute x with (x-1) in D

d. f(x) = x^2(1-x)^2

so f(x-1) = (1-x)^2 (1-(1-x))^2 = (1-x)^2*(x^2) or x^2*(1-x)^2 ->
same as f(x) in the answer choice D.
Director
Joined: 16 Aug 2005
Posts: 950
Location: France
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D is clearly the choice.

Here is how I approached it:

First substitute x=0 and got either C or D as correct.

Then checked against x=5 (or any other integer) and D was the last man standing.

Hence D
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f(x) = 1-x; f(1-x) = 1-(1-x) = x <-- a is out
f(x) = 1-x^2; f(1-x) = 1-(1-x)^2 = 1-(1+2x-x^2) = x^2-2x <-- b is out
f(x) = x^2-(1-x)^2; f(1-x) = (1-x)^2-(1-1+x)^2 = 1-2x+x^2-x^2 = 1-2x <-- c is out
f(x) = x^2(1-x)^2 = (1-x)^2(1-1+x)^2 = (1-x)^2(x^2) <-- d is the answer
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