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# Function Question

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Intern
Joined: 10 May 2009
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02 Jul 2009, 11:45
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For which of the following is 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)

Please give explanations as well. Thanks.

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Manager
Joined: 30 May 2009
Posts: 214

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02 Jul 2009, 11:55
I think this is a GMAT Club question.

F(x) = $$x^2*(1-x)^2$$
Now lets find out what is F(1-x) by substituting 1-x for x in the above equation.

F(1-x) = $$(1-x)^2*(1-(1-x))^2 = (1-x)^2*(x)^2 = (x)^2*(1-x)^2$$
So both F(X) and F(1-x) are same

What is the OA?

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CEO
Joined: 29 Mar 2007
Posts: 2553

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02 Jul 2009, 12:48
delwar2 wrote:
For which of the following is 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)

Please give explanations as well. Thanks.

D.

1-x =/ 1-(1-x)

1-x^2 =/ 1-(1-x)^2

(1-x)^2-(1-(1-x))^2 --> (1-x)^2-x^2 close but not equal to x^2-(1-x)^2

(1-x)^2(1-(1-x)^2 --> (1-x)^2*x^2

Thus D.

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Re: Function Question   [#permalink] 02 Jul 2009, 12:48
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