(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
Let f (x) = ax ^ 2 + BX + C, from F (0) = 1 to C = 1; from F (x + 1) - f (x) = a (x + 1) ^ 2 + B (x + 1) + C - [x ^ 2 + BX + C] = 2aX + A + B = 2x, so 2A = 2, a + B = 0. From the solution, we get a = 1, B = - 1; then f (x) = x ^ 2-x + 1. (2) from x ^ 2-16 >
RELATED INFORMATIONS
- 1. If f (x) is a quadratic function and f (0) = 1, f (2x + 1) - f (x) = 2, find f (x)
- 2. 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)]
- 3. 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)
- 4. 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
- 5. Given that the quadratic function f (x) satisfies the conditions f (0) = 1, f (x + 1) - f (x) = 2x, the number of solutions of F (| x |) = a, a belonging to R is discussed
- 6. Given a = 2010, B = 2012, find quarter a & # 178; - half AB + quarter B & # 178;
- 7. In the indefinite integral of higher mathematics, is the order of u determined in the method of integration by parts against the power exponent three or against the power exponent three Please give an example to explain whether "three" can reach "Zhi", or "Zhi" can reach "three",
- 8. It is fast to find the indefinite integral Thank you Wrong. It's the power of the square of e ^ (- t)
- 9. If A-B = 2, B-C = 1, then a & # 178; + B & # 178; + C & # 178; - AB BC AC= Hurry!
- 10. Calculation: (B-C) / (A & # 178; - AB AC + BC) - (C-A) / (B & # 178; - BC AB + AC) + (a-b) / (C & # 178; - AB BC + AB)
- 11. Let the minimum value of quadratic function y = f (x) be 4, and f (0) = f (2) = 6
- 12. 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
- 13. 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
- 14. 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
- 15. 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
- 16. 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
- 17. 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
- 18. 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
- 19. 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
- 20. 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___ .