It is known that the domain of definition of function f (x) is (0, positive infinity). When x > 1, f (x) > 0, and f (XY) = f (x) + F (y) 1. Find f (1); 2. Prove that f (x) is an increasing function in the domain of definition; 3. If f (1 / 3) = - 1, find the value range of X satisfying the inequality f (x) - f (1 / (X-2)) ≥ 2 Focus on the third question! express thanks on one's knees

It is known that the domain of definition of function f (x) is (0, positive infinity). When x > 1, f (x) > 0, and f (XY) = f (x) + F (y) 1. Find f (1); 2. Prove that f (x) is an increasing function in the domain of definition; 3. If f (1 / 3) = - 1, find the value range of X satisfying the inequality f (x) - f (1 / (X-2)) ≥ 2 Focus on the third question! express thanks on one's knees

1) F (1) = 0; 2) let Y > 1, x > 0, then XY > x > 0, f (XY) - f (x) = f (y) > 0, so f (x) increases monotonically in its domain of definition. 3) 2 = - 2F (1 / 3) = - f (1 / 9) is substituted into the inequality, and f (x) + F (1 / 9) & gt; = f (1 / (X-2)), then f (x / 9) & gt; = f (1 / (X-2)), and from (2) we know that f (x) is an increasing function, so x / 9 {%