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Function

by JeetGulia » Sun Sep 12, 2010 3:55 am
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)

Ans D
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by Rahul@gurome » Sun Sep 12, 2010 4:26 am
Best approach is to start from the last choice. So, start from option (E).
(E) f(1 - x) = (1 - x)/[1 - (1 - x)] = (1 - x)/x, which is not equal to f(x).

(D) f(1 - x) = (1 - x)^2 * [1 - (1 - x)]^2 = (1 - x)^2*(x^2), which is the same as f(x).

The correct answer is [spoiler](D)[/spoiler].
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