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functions

by gmatgirl12 » Tue Oct 27, 2009 7:14 pm
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)

I wasn't even sure where or how to begin this problem. Any advice?

Thank you.
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by CrackGMAC » Wed Oct 28, 2009 6:33 am
Its D. Very simple.

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

Hence, f(x)=f(1-x) for all x
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by mp2437 » Wed Oct 28, 2009 7:06 am
This was solved in another thread, but in any case,
just try plugging in any number, i.e: x = 2.
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