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For which of the following functions is f(x)=f(1-x) for all

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Manager
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For which of the following functions is f(x)=f(1-x) for all [#permalink] New post 06 May 2008, 16:53
For which of the following functions 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)

OA is D. Please explain your answer. Thanks!
Senior Manager
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Joined: 20 Feb 2008
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Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross
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Re: A GMATPrep Question [#permalink] New post 06 May 2008, 17:42
Hi this may not be the quickest way but it can be done within 2 mins.

f(x)=f(1-x)

plug in numbers:
Which equation follows the rule that f(2)=f(1-2)=f(-1)

If you plug in the values of f(2) and f (-1) into each equation you will find that only equation D satisfies this rule.

Therefore the answer should be D
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Re: A GMATPrep Question [#permalink] New post 06 May 2008, 17:43
Replace x by 1-x and your answer should still look like it was earlier.

You can do for all but I am doing just for your answer.
In this equation replace x by 1-x f(x) = (x^2)*((1-x)^2)
you get f(1-x) = (1-x)^2*((1-1+x)^2) = (1-x)^2*x^2 which is same as f(x)

So you have the answer D.
Re: A GMATPrep Question   [#permalink] 06 May 2008, 17:43
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For which of the following functions is f(x)=f(1-x) for all

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