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

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For which of the following functions f is f(x)= f(1-x) for [#permalink]  20 Nov 2005, 05:33
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For which of the following functions f is f(x)= f(1-x) for all x
F(x)=1-x
F(x)=1-x^2
F(x)=x^2-(1-x)^2
F(x)=(x^2) (1-x^2)
F(x)-x/ 1-x
Director
Joined: 14 Sep 2005
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Should be D. F(x)=(x^2) (1-x^2)

D. is the only function which is the greatest at 1/2.

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Intern
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Re: OG PS - Functions - Diff one-methinks ;-) [#permalink]  20 Nov 2005, 10:12
njss750 wrote:
For which of the following functions f is f(x)= f(1-x) for all x
F(x)=1-x
F(x)=1-x^2
F(x)=x^2-(1-x)^2
F(x)=(x^2) (1-x^2)
F(x)-x/ 1-x

I remember seeing this problem in a GMATprep test. I think choice D should be F(x)=(x^2) (1-x)^2. If that is true then substituting (1-x) for will give us the same function back and the answer choice is D, where the function is multiplicative
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