![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
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______ ．
∵ function f (x) is an odd function and a decreasing function on (- ∞, + ∞) ∵ X1 + x2 ＞ 0, X2 + x3 ＞ 0, X3 + x1 ＞ 0, ∵ x1 ＞ - X2, X2 ＞ - x3x3x3 ＞ - x1, ∵ f (x1) ＜ f (- X2,) f (x2) ＜ f (- x3), f (x3) ＜ f (- x1) ∵ f (x1) + F (x2) ＜ 0, f (x2) + F (X3
RELATED INFORMATIONS
- 1. 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
- 2. 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
- 3. 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
- 4. 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
- 5. 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)=
- 6. It is known that f (x) is an odd function defined on R. when x ≥ 0, f (x) = x & sup2; - 2x, then
- 7. 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
- 8. Let f (x) be an odd function defined on R
- 9. For an odd function defined on R, when x > 0, f (x) = x ^ 2-2x + 1
- 10. 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
- 11. 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)______ ．
- 12. It is known that the domain of function FX is [0,4] to find the domain of Y + F (x + 3) + FX It is known that the domain of F (x) is the domain of y = f (x + 3) + F (x ^ 2)
- 13. Let f (x) be an odd function defined on R, and if x > 0, f (x) = x ^ 2-3x, then f (- 2) =?
- 14. Let f (x) be an odd function defined on R, and if x is greater than 0, f (x) = 3x + 1, find the analytic expression of F (x)
- 15. Let f (x) be an odd function defined on R, and if x > 0, f (x) = 3-2 ^ x, then f (- 2)=（ Let f (x) be an odd function defined on R, and if x > 0, f (x) = 3-2 ^ x, then f (- 2)=（
- 16. Let f (x) be an odd function defined on R, f (x + 3) f (x) = - 1 Since a function is an odd function defined on R, why let x = 0. F (x) = 0 such that f (x + 3) f (x) = - 1 does not hold?
- 17. Let f (x) be an odd function defined on R. when x < 0, f (x) = x23, then f (8)=______ ．
- 18. Let f (x) be an odd function, and if x is greater than 0, f (x) = x-3-2x-1, then the expression of F (x) on X ∈ R is obtained
- 19. If f (x) is an odd function defined on R, then
- 20. If f (x) is an odd function on R, and if x > 0, f (x) = the third power of X + 1, then the expression of F (x) is