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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
f（x-1）+f（x^2-1）＜0
f(x^2-1)
RELATED INFORMATIONS
- 1. 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,
- 2. 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
- 3. 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
- 4. 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______ ．
- 5. 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
- 6. Known function FX = x ^ 2-4x + 6, x > = 0, FX = 2x + 4, X
- 7. 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
- 8. FX is an odd function defined on R, XF '(x) + F (x) on (- infinity, O)
- 9. If f (x) is an odd function defined on R and is an increasing function in (0, + ∞), and f (2) = 0, then the solution set of the inequality XF (x) < 0 is______ ．
- 10. It is known that the function f (x) is a monotone increasing function defined on (0, ∞), and f (XY) = f (x) + F (y) for any X and Y in the domain of definition f（3）=1. (1) Finding the value of F (1) (2) Solving inequality f (3x) + F (2x-1) ≤ 2
- 11. 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
- 12. 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
- 13. For an odd function defined on R, when x > 0, f (x) = x ^ 2-2x + 1
- 14. Let f (x) be an odd function defined on R
- 15. 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
- 16. It is known that f (x) is an odd function defined on R. when x ≥ 0, f (x) = x & sup2; - 2x, then
- 17. 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)=
- 18. 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
- 19. 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
- 20. 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