If the differentiable function f (x) defined on (0, + ∞) satisfies: X · f '(x) < f (x) and f (1) = 0, then the solution set of F (x) x < 0 is () A. (0,1)B. (0,1)∪(1,+∞)C. (1,+∞)D. ϕ

If the differentiable function f (x) defined on (0, + ∞) satisfies: X · f '(x) < f (x) and f (1) = 0, then the solution set of F (x) x < 0 is () A. (0,1)B. (0,1)∪(1,+∞)C. (1,+∞)D. ϕ

The definition field of function f (x) is x > 0, so when f (x) < 0, f (x) < 0, XF '(x) < f (x), then XF' (x) < 0, ∵ x > 0 ∵ f '(x) < 0 ∵ function f (x) is a decreasing function on (0, + ∞), and