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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 _________________
"To dream anything that you want to dream, that is the beauty of the human mind. To do anything that you want to do, that is the strength of the human will. To trust yourself, to test your limits, that is the courage to succeed."
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.