Determine all functions f : R -->> R, where R is the set of all real numbers, satisfying the following 2 conditions:
(i) There exists a real number M such that for every real number x, f(x) < M is satisfied ,
(ii) For every pair of real numbers x and y, f(xf(y)) + yf(x) = xf(y) + f(xy) is satisfi ed .
<<< 2011 APMO Prob >>>
(i) There exists a real number M such that for every real number x, f(x) < M is satisfied ,
(ii) For every pair of real numbers x and y, f(xf(y)) + yf(x) = xf(y) + f(xy) is satisfi ed .
<<< 2011 APMO Prob >>>
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