For an odd function defined on R, when x > 0, f (x) = x ^ 2-2x + 1

F (x) is an odd function on R,
f(x)=-f(-x)
x>0,f(x)=x^2-2x+1
x0
f(-x)=(-x)^2-2(-x)+1
=x^2+2x+1
=-f(x)
f(x)=-f(-x)
=-x^2-2x-1
The analytic expression of the function is:
f(x)=x^2-2x+1(x>0)
f(x)=0,x=0
f(x)=-x^2-2x-1,(x

RELATED INFORMATIONS

1. It is known that the function f (x) is an odd function whose domain of definition is R. when x > 0, f (x) = x-x + 1, then if x
2. It is known that the function f (x) is an odd function in the domain (- 2,2). The odd function in the interval [0,2] decreases monotonically in the interval [0,2] Solve the inequality f (x-1) + F (x ^ 2-1) < 0
3. It is known that the function f (x) is an odd function in the domain of definition (&; - 2,2) It is known that the function f (x) is an odd function in the domain of definition (&; - 2,2) and increases monotonically in the interval [0,2]. The solution to the inequality f (x-1) + F (x ^ 2-1) < 0 The answer is (- 1,1), why
4. Given that f (x) is an odd function in the domain of definition on the interval [1, - 1] and is an increasing function, the value of F (0) can be obtained,
5. When x > 0, the function FX is meaningful and satisfies F 2 = 1, f (XY) = FX + FY, FX is an increasing function (1) Verification: F (1) = 0 (2) If f (3) + F (4-8x) > 2, find the value range of X
6. If the function FX defined on R satisfies f (x + y) = f (x) + F (y) + 2XY [XY belongs to R] f (1) = 2, then f (- 2) =? Please be more detailed! 20 points will be sent! If it's OK, points will be added! The earlier you answer, the more points will be added. Thank you
7. For the function f (x) defined on the interval D, if ∀ x1, X2 ∈ D, and X1 & lt; X2, there is & nbsp; If f (x 1) ≥ f (x 2), then f (x) is a "non increasing function" on interval D. if f (x) is a "non increasing function" on interval [0,1] and f (0) = L, f (x) + F (l-x) = L, then f (x) ≤ - 2x + 1 holds when x ∈ [0,14]. There are the following propositions: ① ∀ x ∈ [0,1], f (x) ≥ 0; ② when x1, X2 ∈ [0,1] and x1 ≠ X2, f (x 1) ≠ f (x) ③ f (18) ）+F (511) + F (713) + F (78) = 2; 4. When x ∈ [0,14], f (f (x)) ≤ f (x). Where the serial numbers of all propositions that you think are correct are______ ．
8. The definition of function monotonicity is as follows: if X1 is less than x2 and FX1 is less than or equal to FX2, then the function is monotone increasing function. Why is there equal to in the definition
9. Known function FX = x ^ 2-4x + 6, x > = 0, FX = 2x + 4, X
10. Function FX = 1 / 4 ^ x + m (M > 0), when X1 + x2 = 1, FX1 + FX2 = 1 / 2, 1, find the value of M 2. The known sequence an satisfies an = F0 + F (1 / N) + F (2 / N) + +F (n-1 / N), find an 3, if Sn = a1 + A2 + a3 + +An, Sn 4 ^ x + m is the denominator x1, and X2 belongs to R
11. Let f (x) be an odd function defined on R
12. It is known that the function y = f (x) is an odd function defined on R. when x0, the analytic expression of F (x) is obtained (2) Are there real numbers a and B (where 0 ≤ a ＜ b) such that the value range of F (x) on [a, b] is [a, b]? If so, find out all the values of a and B. if not, explain the reason
13. It is known that f (x) is an odd function defined on R. when x ≥ 0, f (x) = x & sup2; - 2x, then
14. It is known that F X is an odd function defined on R and satisfies f (x 4) = f (x). When x ∈ (0,2), f (x) = 2x & sup2;, then f (7)=
15. It is known that f (x) is an odd function defined on R. when x ≥ 0, f (x) = 2x-x & sup2 (1) Finding the expression of function f (x) (2) If x ∈ [a, b], f (x) ∈ [1 / B, 1 / a], if 0
16. Let f (x) be an odd function defined on R, and if x ≥ 0, f (x) decreases monotonically. If x 1 + x 2 > 0, then the value of F (x 1) + F (x 2) () A. Constant negative B. equal to zero C. constant positive D. unable to determine positive or negative
17. Let f (x) be an odd function defined on R, and f (- 1) = 0, if the inequality x1f (x1) - X2F (x2) / x1-x2 ＜ 0 pairs of interval (- infinite, 0) If any two unequal real numbers x 1 and x 2 hold, then the solution set of the inequality x f (2x) < 0 is
18. It is known that f (x) is an odd function on R and a decreasing function. If X1 + x2 > 0, X2 + X3 > 0, X3 + X1 > 0, then the value of F (x1) + F (x2) + F (x3) () A. Must be greater than zero B. must be less than zero C. is zero D. both positive and negative are possible
19. Given that f (x) is an odd function and a decreasing function on (- ∞, + ∞), and X1 + x2 > 0, & nbsp; & amp; X1 + X3 > 0, X2 + X3 > 0, then the relation between F (x1) + F (x2) + F (X3) and 0 is zero______ ．
20. It is known that the odd function f (x) defined on R is a decreasing function. If X1 + x2 < 0, X2 + X3 < 0, X3 + X1 < 0, then the value of F (x1) + F (x2) + F (x3)______ ．