It is known that y = f (x) is an odd function defined on R. when x ≥ 0, f (x) = x2-2x, then the expression of F (x) on R is () A. -x（x-2）B. x（|x|-2）C. |x|（x-2）D. |x|（|x|-2）

Let x < 0, then - x > 0, ∵ when x ≥ 0, f (x) = x2-2x, ∵ f (- x) = (- x) 2-2 (- x) = x2 + 2x, and ∵ y = f (x) is an odd function defined on R, f (- x) = - f (x), ∵ f (x) = x2 + 2x, ∵ f (x) = - x2-2x, so the expression of F (x) on R is x (| x | - 2), so B

RELATED INFORMATIONS

1. It is known that f (x) is an odd function defined on R. when x > 0, f (x) = x ^ 2-2x + 1, then the expression of F (x) is Its function-
2. When X & gt; 0, FX = - x + 1, then when X & gt; 0, the expression of FX is?
3. Given that the domain of definition of odd function f (x) is r, and for any real number x, f (x + 2) = - f (x), and f (1) = 4, then f [f (2015)]=
4. For any odd function FX on the domain R, there are a. f (x) - (F-X) > 0, B. f (x) - f (- x) ≤ 0, C. f (x) × f (- x) ≤ 0, D. f (x) × f (- x). Why choose C
5. If f (x + 1) and f (x-1) are both odd functions, and f (0) = 2, then what is f (4)
6. If f (x) = radical √ x ∧ 2 + 3x-4 and G (x) = radical √ X-1 + radical √ x + 4 are defined as a and B respectively, then the relationship between a and B is a. a The definition field of function f (x) = radical √ x ∧ 2 + 3x-4 is a, and the definition field of function g (x) = radical √ X-1 + radical √ x + 4 is B, then the relationship between a and B is A. A does not include B. B. A = B. CA includes B. Da includes B
7. It is known that the piecewise function f (x) is an odd function on R. when x > 0, f (x) = x2-2x + 3, the analytic expression of F (x) is obtained
8. The definition field of function f (x) = x + 1 is [1,16], f (x) = f (2x) + f ^ 2 (x) + 1. Find the value field of function f (x)
9. The definition domain of function f (x) is (- ∞, 1) ∪ (1, + ∞), and f (x + 1) is an odd function. When x > 1, f (x) = 2x2-12x + 16, then the value range of real number m with two zeros of equation f (x) = m is () A. （-6，6）B. （-2，6）C. （-6，-2）∪（2，6）D. （-∞，-6）∪（6，+∞）
10. If the function f (x) has f (2 + x) = f (2-x) for any real number x, and the equation f (x) = 0 has four real roots, then the sum of the four real roots?
11. 5. Given that f (x) is an odd function defined on R, when x ≥ 0, f (x) = x-2x, find the expression of F (x) on R 5. Given that f (x) is an odd function defined on R, when x ≥ 0, f (x) = x-2x, find the expression of F (x) on R 6. It is known that the function f (x) is an even function on R. when x ≥ 0, f (x) = x-2x-3 (1) Write the expression of function y = f (x) with piecewise function; (2) Using symmetry to draw its image; (3) The monotone interval is pointed out; (4) It is pointed out that in what interval f (x) > 0 and in what interval f (x) < 0 by using images; (5) Find the maximum value of the function 7. Find the range of function y = 1 / X (x ＞ - 4 and X is not equal to 0) 8. Find the range and monotone interval of the function y = | x + 2 | - | X-5 | 9. It is known that the function y = f (x) is an even function defined on R. when x < 0, f (x) is monotonically increasing. The solution set of the inequality f (x + 1) > F (1-2x) is obtained 10. The definition field of function y = x-3x-4 is [0, M], the range of value is [- 25, 4, - 4], and the value range of real number m is obtained
12. Given that the function defined on (0, -∞) satisfies f (x, y) = f (x) + F (y), and if x > 1, f (x) < 0, if f (half) = 1, find the solution set of the inequality f (x) + F (5-x) ≥ - 2 Is f (XY) = f (x) + F (y)
13. It is known that the domain of F (x) is r, and its derivative satisfies 0
14. It is proved that if the function f (x) is a strictly increasing function on [a, b], then the equation f (x) = 0 has at most one real root on the interval [a, b]
15. For any differentiable function f (x) on R, if x is not equal to 1 and satisfies (x-1) f '(x) > 0, it is proved that f (0) + F (2) > 2F (1)
16. Let f (x) be differentiable on [0,1] and 0
17. The function f (x) is differentiable on [0,1] and 0
18. The function f (x) = x / (AX + b) (a, B are non-zero real constants) satisfies that f (2) = 1 and the equation f (x) = x has only one solution 1. Find the value of a and B. We already know that a = 0.5, B = 1 2. Is there a real constant M, n such that for any x, f (x) + F (M-X) = n constant in the domain of definition? If so, find out the value of M, N. if not, explain the reason
19. Given that the function f (x) = x divided by ax + B (a, B is constant and a ≠ 0) satisfies f (2) = 1, the equation f (x) = x has a unique solution, find the function f (x) And find the value of F (f (- 3))
20. Given the function f (x) = x2ax + B (a, B are constants) and the equation f (x) - x + 12 = 0 has two real roots X1 = 3, X2 = 4. (1) find the analytic expression of function f (x); (2) let k > 1, solve the inequality about X; f (x) ＜ (K + 1) x-k2-x