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Though the easier way if to simply scan through the ans choices and D comes across as an easy answer, i am posting the detailed soln as well.

A) f(1-x) = 1-(1-x) = x
B) f(1-x) = 1-(1-x)^2 not equal to 1-x^2 for all values of x
C) f(1-x) = (1-x)^2 - x^2 = 1-2x not equal to f(x)
D) Correct
E) f(1-x) = (1-x)/x not equal to f(x) for all x

Got D...in around 90 seconds. Didn't scan..worked it out in reverse order. Trust ETS to make me work through all the answer choice and keep the answer at D or E.

Infact functions of this type are called symmetric functions. A function that is unchanged by any permutation of its variables.

Egs:
f(x,y) = x*y
f(x,y) = x+y
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I have no idea what this question is asking for. Can some one explain this question? Oh, and sorry for the broad question, I don't even know what to ask.