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Source: — Problem Solving |
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by Mani_mba » Fri Sep 26, 2008 11:02 am
To prove: f(x) = f(1-x)

A) f(x)=1-x
f(1-x) = 1-(1-x) = x
=> f(x) <> f(1-x)

B) f(x) = 1-x^2
f(1-x) = 1-(1-x)^2 = 1-(1+x^2-2x) = 2x - x^2
=> f(x) <> f(1-x)

c) f(x) = x^2-(1-x)^2 = 2x-1
f(1-x) = 2(1-x)-1 = 1-2x
=> f(x) <> f(1-x)

D) f(x) = x^2(1-x)^2
f(1-x) = (1-x)^2(x^2)
=> f(x) = f(1-x)

E) f(x) = x/(1-x)
f(1-x) = (1-x)/x
=> f(x) <> f(1-x)

Hence D.

HTH.
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by cramya » Fri Sep 26, 2008 9:34 pm
I am not sure what post u were referring to but here it goes

Pick numbers (somehting easy to work with other than 0 or 1)

Lets say x = 2 therefore 1-x = -1

Only D) will be true.
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