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【简答题】
已知定义在（-1，1）上的函数f （x）满足 f( 1 2 )=1 ，且对x，y∈（-1，1）时，有 f(x)-f(y)=f( x-y 1-xy ) ． （I）判断f（x）在（-1，1）上的奇偶性，并证明之； （II）令 x 1 = 1 2 ， x n+1 = 2 x n 1+ x 2n ，求数列{f（x n ）}的通项公式； （III）设T n 为数列 { 1 f( x n ) } 的前n项和，问是否存在正整数m，使得对任意的n∈N * ，有 T n ＜ m-4 3 成立？若存在，求出m的最小值；若不存在，则说明理由．
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