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Function Problem

by chiangka » Sat Apr 16, 2011 1:00 pm
Found this to be surprisingly confusing... any help in understanding exactly what is being asked would be greatly appreciated!

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)

Thanks!

Answer:
d
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by Target2009 » Sat Apr 16, 2011 1:14 pm
its D.

Simply Put f(x) = x^2 (1-x)^2
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by manpsingh87 » Sat Apr 16, 2011 8:34 pm
chiangka wrote:Found this to be surprisingly confusing... any help in understanding exactly what is being asked would be greatly appreciated!

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)

Thanks!

Answer:
d
lets analyze each option individually,
A)f(x)=1-x, f((1-x)=1-(1-x)=x; hence f(x) is not equal to f(1-x);
B)f(x)=1-x^2, f(1-x)=1-(1-x)^2=1-1-x^2+2x=2x-x^2 hence f(x) is not equal to f(1-x);
C)f(x)=x^2-(1-x)^2, f(1-x)=(1-x)^2-(1-1+x)^2=(1-x)^2-x, f(x)=-f(1-x);
D)f(x)=x^2(1-x)^2; f(1-x)=(1-x)^2(1-1+x)^2, f(1-x)=(1-x)^2 x^2, hence f(x)=f(1-x);
E)f(x)=x/(1-x); f(1-x)=1-x/1-1+x, 1-x/x, here f(1-x)=1/f(x);

as seen above only for option D we have f(x)=f(1-x); hence D
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