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

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Intern
Joined: 14 May 2008
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For which of the following functions f is f(x)=f(1-x) for [#permalink]

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05 Jun 2008, 23:03
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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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VP
Joined: 18 May 2008
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05 Jun 2008, 23:34
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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Manager
Joined: 31 Oct 2007
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05 Jun 2008, 23:49
D

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

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Director
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06 Jun 2008, 00:04
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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Manager
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22 Jun 2008, 12:32
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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Manager
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24 Jun 2008, 01:22
i did it substitution. Any other solutions?

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Current Student
Joined: 12 Jun 2008
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24 Jun 2008, 03:00
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 ?

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Re: For which   [#permalink] 24 Jun 2008, 03:00
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For which of the following functions f is f(x)=f(1-x) for

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