The function f (x) defined in positive integer set has f (M + n) = f (m) + F (n) + 4 (M + n) -· 2 for any m, N, and f (1) = 1 If m ^ 2-tm-1

Let m = x, n = 1, f (x + 1) = f (x) + 4x + 3; so: F (2) = f (1) + 4 * 1 + 3f (3) = f (2) + 4 * 2 + 3f (4) = f (3) + 4 * 3 + 3. F (x) = f (x-1) + 4 * (x-1) + 3, f (x) = f (1) + 4 * (1 + 2 + 3 +... + (x-1)) + 3 * (x-1) = 2x & sup2; + X-2. Obviously, the minimum value of F (x) is 1, so M & sup2; - TM-1

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1. For any m, n ∈ n +, f (M + n) = f (m) + F (n) + 4 (M + n) - 2, f (1) = 1 1. Find the expression of F (x) 2. M ∧ 2-tm-1 ≤ f (x) for any m ∈ [- 1,1], X ∈ n + is constant, find the value range of real number t
2. The function y = f (x) defined on positive integer set has f (a + b) = f (a) * f (b) constant for any a, B ∈ n Let f (1) = a ≠ 0, if an = f (n) (n ∈ n +) (1) Prove: the sequence {an} is an equal ratio sequence, and find out the general term formula of the sequence {an} (2) If Sn = a1 + A2 + +An, the sequence {sn-2an} is an equal ratio sequence, find the value of real number a
3. 6. Given that the function f (n) defined on a positive integer satisfies the following condition (1) f (M + n) = f (m) + F (n) + Mn (2) f (3) = 6, then f (2000) =?
4. It is known that a set M is a set of functions f (x) satisfying the following two properties simultaneously ① F (x) is a monotone increasing function or a monotone decreasing function in its domain of definition; ② There is an interval [a, b] in the domain of F (x), such that the range of F (x) on [a, b] is [A / 2, B / 2] (1) Judge whether the function f (x) = √ x belongs to m? And explain the reason. If so, request the interval [a, b]; (2) If the function f (x) = √ (x-1) + T ∈ m, find the value range of real number t Be as detailed as possible
5. If the points (1, m), (- 2, n) are all on the image of the function y = - x + 2, then the value of Mn is?
6. If the intersection point of the image of function y = x + m and function y = NX + 2 is on the X axis, then Mn=————
7. Given the function f (3x) = 3x + 2, then f (x) is equal to
8. Let f (x) = x2-3x + 1, then f (a) - f (- a) is equal to =?, Urgent,,
9. Given the complete set I = R, set a = {x | x ^ 2 + 3x + 2 = 0}, B = {x | x ^ 2 + (M + 1) x + M = 0}. If CIA intersection B = Φ, find the value of M
10. Given that the domain of definition of function y = radical X & # 178; - 2aX + 2 is r, find the range of real number a
11. A function f (x) defined on a positive integer set has f (M + n) = f (m) + F (n) + 4 (M + n) - 2 for any m, n ∈ n *, and f (1) = 1 (1) Find the expression of function f (x); (2) If m ^ 2-tm-1 ≤ f (x) belongs to [- 1,1] for any m and X belongs to n * constant, the value range of real number T is obtained; (3) For any positive integer n, there are always m + 1 real numbers A1, A2,... In [2, N + 16 / N] , am, am + 1, so that f (A1) + F (A2) + +f(am)
12. If u = {1,2,3,4,0}, a = {1,2,3}, B = {2,4}, then cuaub is A{0,2,4} B{2,3,4} C{1,2,4} D{0,2,3,4}
13. Let u = {1,2,3,4}, a = {x vertical line X & # 178; - 5x + M = 0} If a is contained in U, find the range of M The answer is m = 4 or M = 6 or m greater than 25 out of 4
14. Given the complete set u = {1,2,3,4,5}, a = {x | x2-5x + M = 0}, B = {x | x2 + NX + 12 = 0}, and (∁ UA) ∪ B = {1,3,4,5}, can you find the value of M + n?
15. (2a + b) (2a-3b) + 3A (2a + b) and X (x + y) (X-Y) - x (x + y) &; 4a (x + y) - 6x-6y and a (a-b) - AB + B & # 178;
16. Calculate 2A · (x-3a) = (x + 1) (X & # 178; - x + 1) Calculate the following questions - 2 / 3x & # 178; Y (2x-3 / 1xy + Y & # 178;), (3x-2y) & # 178; · (3x + 2Y) & # 178;
17. X & # 178; - 4ax + 3A & # 178; = 1-2a Does X have a real number
18. Let a = {X & # 178; + (2a-3) x-3a = 0}, B = {X & # 178; + (A-3) x + A & # 178; - 3A = 0}, if a ≠ B, a ∩ B ≠ empty set, try to find a ∪ B
19. Given the set a = {x | 2A ≤ x ≤ A & # 178; + 1}, B = = {x | X & # 178; - 3 (a + 1) x + 2 (3a + 1) ≤ 0} a ∈ R, if B contains the range of a for a?
20. The known set a = {X / x ^ 2-4ax + 3A ^ 2