The quadratic function f (x) = ax ^ 2 + (A-1) x + A is known The function g (x) = f (x) + (1 - (A-1) x ^ 2) / X is an increasing function on (2,3). Find the value range of real number a

RELATED INFORMATIONS

• 1. The quadratic function f (x) = ax ^ 2 + X is known Given quadratic function f (x) = ax ^ 2 + X (a belongs to R, a ≠ 0) (1) For any x1, X2 ∈ R, compare the size of 1 / 2 * [f (x1) + F (x2)] and f [(x1 + x2) / 2] (2) If x belongs to [0,1], with absolute value f (x) ≤ 1, the value range of a is obtained
• 2. It is known that the quadratic function y = f (x) satisfies f (- 2) = f (0) = 0, and the minimum value of F (x) is - 1 (1) If the function y = f (x), X ∈ R is an odd function, when x > 0, f (x) = f (x), find the analytic expression of the function y = f (x), X ∈ R (2) Let g (x) = f (- x) - t · f (x) + 1. If G (x) is a decreasing function on [- 1,1], the value range of real number T is obtained
• 3. Given the quadratic function y = f (x), satisfying f (- 2) = f (0) = 0, and the minimum value of F (x) is - 1. (1) if the function y = f (x), X ∈ R is odd, when x > 0, f (x) = f (x), find the analytic expression of the function y = f (x), X ∈ R; (2) Let G (x) = f (- x) - λ f (x) + 1, if G (x) is a decreasing function on [- 1, 1], find the value range of real number λ
• 4. It is known that the quadratic function f [x] satisfies f [2-x] = f [2 + x], and the intercept of the image on the y-axis is 0, and the minimum value is negative one
• 5. Let the minimum value of quadratic function y = f (x) be 4, and f (0) = f (2) = 6
• 6. (1) If f (x) is a quadratic function, and f (0) = 1, f (x + 1) - f (x) = 2x, find (x) (2) The value range of y = radical (x2-16) is
• 7. If f (x) is a quadratic function and f (0) = 1, f (2x + 1) - f (x) = 2, find f (x)
• 8. It is known that the coefficient of quadratic term of quadratic function f (x) is negative, and for any x, it is constant and f (2-x) = f (2 + x) holds. Solve the inequality f [Log1 / 2 (x ^ 2 + X + 1 / 2)]
• 9. It is known that f (1-x) = f (1 + x) holds for any quadratic function f (x) belonging to R Let a = (SiNx, 2), B = (2sinx, 1 / 2), C = (cosx, 1), d = (1,2). When x belongs to [0, π], find the solution set of the inequality f (a × b) > F (C × d)
• 10. It is known that the quadratic function f (x) satisfies f (x + 1) - f (x) = 2x (x ∈ R), and f (0) = 1 It is known that f (x) is a quadratic function. For any x belonging to R, f (x + 1) - f (x) = - 2x + 1 and f (0) = 1 are satisfied (1) Finding the analytic expression of F (x) (2) When x belongs to [- 2,1], the image of y = f (x) is always above the image of F = - x + m, and the value range of real number m is obtained I would like to ask the following constant set up into a solution Is m ∈ [- 1,5] the answer? (2) In the question, f (x) = 2x + m has a solution, and the range of real number m is obtained
• 11. It is known that y = f (x) is a quadratic function and f (- 2 / 3-x) = f (- 2 / 3 + x), which holds for X ∈ R, F (- 2 / 3) = 49, the difference between the two real roots of the equation f (x) is only 7, (1) find the analytic expression of quadratic function, (2) find the maximum value of F (x) in the interval [T, t + 1], T is a random number, not a fixed value There are three cases where t + 1 is on the left, right and middle of the axis of symmetry
• 12. The quadratic function f (x) = x ^ 2 + (m-1) x + 1, if any x belongs to R, f (x) > 0 is constant, the range of M is obtained
• 13. It is known that the quadratic function y = f (x) and G (x) = x ^ 2 have the same image opening size and direction, and the minimum value of y = f (x) at x = m is - 1 If the maximum value of the function y = f (x) on the interval [- 2,1] is 3, find M
• 14. Given that point a (- A & # 178; - 1, m) and point B (- 1, n) are on the image of quadratic function y = x & # 178;, then the size relation of M and N is___ .
• 15. Given the points a (- 1, m), B (- 2, n) on the image of quadratic function y = - x?, the size of M and N are compared
• 16. Given the points a (- 1, m), B (- 2, n) on the image of quadratic function y = -- X ^, compare the size of M and n
• 17. No matter what the value of M is, the image of quadratic function y = x ^ 2 - (2-m) x + m always passes through the point? Why (1 + x) M = Y-X ^ 2 + 2x find out this step and then how to do it?
• 18. Given the quadratic function y = (x-m) 2 - (x-m), if the vertex coordinates of the quadratic function image is (5 / 2, n), find the value of M, n
• 19. It is known that the image of quadratic function y = x2 + BX + C passes through two points a (n, - 2), B (1, m) on the line y = x-4. (1) find the value of B, C, m, N; (2) find the value of B, C, m, N; (3) find the value of B, C, m, N; (4) find the value of B, C, m, m, N; (4) find the value It is known that the image of quadratic function y = x2 + BX + C passes through two points a (n, - 2), B (1, m) on the line y = x-4 (1) Find the value of B, C, m, n; (2) Judge whether the point C (m, n) is on the image of the quadratic function and explain the reason
• 20. The meaning of algebraic expression According to your life experience, please correct the algebraic formula X / 2 + 3Y