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

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Manager
Joined: 13 Mar 2007
Posts: 98
For which of the following functions is f(x)=f(1-x) for all  [#permalink]

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06 May 2008, 17:53
1
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)

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Senior Manager
Joined: 20 Feb 2008
Posts: 291
Location: Bangalore, India
Schools: R1:Cornell, Yale, NYU. R2: Haas, MIT, Ross

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06 May 2008, 18:42
1
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
Director
Joined: 10 Sep 2007
Posts: 909

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06 May 2008, 18:43
1
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.
Non-Human User
Joined: 09 Sep 2013
Posts: 7747
Re: For which of the following functions is f(x)=f(1-x) for all  [#permalink]

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23 Oct 2017, 16:46
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Re: For which of the following functions is f(x)=f(1-x) for all &nbs [#permalink] 23 Oct 2017, 16:46
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