Let S be the set of real numbers strictly greater than -1.Find all functions f:S->S satisfying the two condition;
(i)f(x+f(y)+xf(y))=y+f(x)+yf(x) for all x and y in S;
(ii)f(x)/x is strictly increasing on each of intervals -1<x<0 and 0<x.
中文版 以英文為準
設 S 係一些大過一的實數.找出所有函數f:S->S合符以下兩個條件;
(i)所有在S的x,y合符f(x+f(y)+xf(y))=y+f(x)+yf(x)
(ii)f(x)/x的值是由-1至正無限不斷上升在這兩個區域-1<x<0 and 0<x.
f:S->S即是說設C=f(x) x大過-1 C都大過-1
唔該哂......