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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] New post 05 Jun 2008, 22:03
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)
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Re: For which [#permalink] New post 05 Jun 2008, 22:34
wht is the explanation?
alpha_plus_gamma wrote:
ekta wrote:
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)


D
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Re: For which [#permalink] New post 05 Jun 2008, 22:49
D

This took a while to solve. Is there a short cut to do this problem under 1.5 minutes?
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Re: For which [#permalink] New post 05 Jun 2008, 23:04
ritula wrote:
wht is the explanation?
alpha_plus_gamma wrote:
ekta wrote:
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)


D


I dunno if mine is the fastest way to do but i did it following way

for value 1, 1-x =0 (for other's if x positive 1-x will be -ve & vice versa)
E and then A & B ruled out.
C too doesn't satisfy. D only held true

(I tested a positive, negative pair with D to confirm)
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Re: For which [#permalink] New post 22 Jun 2008, 11:32
ekta wrote:
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)


Can someone explain the answer to this problem pls.
Thanks!
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Re: For which [#permalink] New post 24 Jun 2008, 00:22
i did it substitution. Any other solutions?
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Re: For which [#permalink] New post 24 Jun 2008, 02:00
snoor wrote:
D

This took a while to solve. Is there a short cut to do this problem under 1.5 minutes?

Just observe that D doesn't change when you replace x by 1-x:

* f(x) = x^2*(1-x)^2
* f(1-x) = (1-x)^2*(1-(1-x))^2 = (1-x)^2*x^2

Don't you see they are the same ? ;)
Re: For which   [#permalink] 24 Jun 2008, 02:00
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