The function defined on R is y = f (x), f (0) is not equal to 0, when x > 0, f (x) > 1, and for any a, B belongs to R, f (a + b) = f (a) f (b) (1) , prove that f (0) = 1; (2), prove that for any x belonging to R, f (x) > 0; (3), prove that f (x) is an increasing function on R; (4), if f (x) * f (2x-x Square) > 1, find X

1. Because f (a + b) = f (a) f (b), let a = b = 0 in the formula: F (0) = f (0) * f (0), because f (0) is not equal to 0, the two equations eliminate f (0) at the same time, and get: F (0) = 1.2. Let f (a + b) = f (a) f (b) where a = b = x / 2, then f (x) = f (0.5x) * f (0.5x) = (f (0.5x)) ^ 2 > = 0

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1. The function defined on R is y = f (x), and f (0) is not equal to 0. When x > 0, f (x) > 1, and for any a and B, f (0) = 1 is proved by F (a + b) = f (a) * f (b) (1) The function defined on R is y = f (x), f (0) is not equal to 0, when x > 0, f (x) > 1, and for any a, B, f (a + b) = f (a) * f (b) (1) Prove that f (0) = 1 (2) prove that for any x belongs to R, f (x) > 0 (3) prove that f (x) is an increasing function on R. 4) if f (x) * f (2x-x2) > 1, find the value range of X
2. The increasing function y = f (x) defined on R has f (x + y) = f (x) + F (y) for any x, y belonging to R Find f (0) To prove that f (x) is an odd function Solving inequality f (3x) + F (x + 1) < 0
3. The function y = f (x) defined on R, when x ＞ 0, f (x) ＞ 1, and for any a, B belongs to R, f (a + b) = f (a) f (b), (1) Find f (0) = 1; (2) Proof: for any x belongs to R, f (x) > 0 (3) It is proved that f (x) is an increasing function on R; (4) If f (x) · f (2x-x2) > 1, find the value range of X
4. It is known that the range of the function f (x) = 1 / 2x ^ 2-x + 3 / 2 defined on [1, M] is also [1, M], then the value of the real number m is
5. Let f (x) = - 2x ^ 2 + 7X-2, for real number m (0 < m < 7 / 4), if the domain of definition and value of F (x) are [M, 3] and [1,3 / M] respectively, what is the value of M?
6. It is known that the function f (x) is a decreasing function in the domain of definition (- infinity, 4) and can make f (m-sinx) ≤ f (1 + 2m) - 7 / 4 under the root sign)
7. It is proved that the function f (x) = - x ^ 3 + 1 is a monotone decreasing function on R
8. It is proved that the function f (x) = - x 3 + 1 is a decreasing function on (- ∞, + ∞)
9. F (x) is an odd function and an increasing function in the interval (0, positive infinity), and f (- 2) = 0, f (x-1)
10. It is known that the function y = f (x) is an odd function on R and an increasing function on (0, + ∞). It is proved that: (1) f (0) = 0; (2) y = f (x) is also an increasing function on (- ∞, 0)
11. Given that | B-5 | + (a + 6) 2 = 0, a and B are rational numbers, then (a + b) + (a + b) 2 + (a + b) 3 + +(a + b) two thousand nine power + (a + b) 2010 power +(a + b) 2011 power
12. Given that the image of power function y = f (x) passes through point (4,2) 1, the analytic expression of F (x) is
13. If the image of power function y = f (x) passes through point (2,2), then f (9)=______ ．
14. Given the power function y = f (x), if the image passes 9 (2, root 2), then f (9) =?
15. Given that the image of power function y = f (x) passes through point (9,1 / 3), find the value of F (36) Process is the most important thing
16. Given the power function y = f (x), the image passes through the point (9, one third) to find the value of F (36)
17. If the polynomial MX ^ 3 + 3nxy ^ 2-2x ^ 3 + XY ^ 2 + y contains no cubic term, then 2m + 3N =?
18. Given the power function f (x) = x ^ m, and f (2)
19. If f (x) = (M & # 178; - m-1) x ^ (M & # 178; + m + 3) is a power function, and if x ∈ (0, positive infinity), f (x) is an increasing function, find the analytic expression of F (x)?
20. If the maximum value of a function y = (M & # 178; - 1) x + M & # 178; - 5m-6 in the closed interval [- 1,2] is 1, find the value of M