The function f (x) defined on (- 1,1) satisfies: for any x, y belonging to (- 1,1), there is f (x) + F (y) = f (x + Y1 + XY). (1) proof: the function f (x) is an odd function! (2) If x belongs to (- 1,0), f (x) > 0. Prove that f (x) is a decreasing function on (- 1,1)

The function f (x) defined on (- 1,1) satisfies: for any x, y belonging to (- 1,1), there is f (x) + F (y) = f (x + Y1 + XY). (1) proof: the function f (x) is an odd function! (2) If x belongs to (- 1,0), f (x) > 0. Prove that f (x) is a decreasing function on (- 1,1)

(1) Let x = y = 0, we get f (0) + F (0) = f (0) and f (0) = 0. Let y = - x, we get f (x) + F (- x) = f (0) = 0, f (- x) = - f (x), and the function f (x) is odd. (2) let - 1 < X1 < x2 < 1, then f (x1) − f (x2) & nbsp; = f (x1) & nbsp; + F (− x2) & nbsp; = f