It is known that f (x) is an odd function over R, and if x

Let x + 1 = t X

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1. Prove that cosh (3x) = 4 * (coshx) ^ 3 + 3 * coshx
2. What is the number of functions whose range is {2,5,10}, where the corresponding relation is y = x ^ 2 + 1 A.1 B.8 C.27 D.39 This is the joint examination of ten schools in Ningbo, Zhejiang Province in 2009
3. Find the range of function y = 10 ^ X-10 ^ (- x) / 10 ^ x + 10 ^ (- x)
4. Find the range of the following functions y = x + √ x + 1 f (x) = (x + 5) / (X & # 178; + 4) Don't be wrong
5. The range of the function f (x) = - X & # 178; - 2x + 5 is
6. The range of function f (x) = (X & # 178; + X + 1) / (X & # 178; + 1) is
7. The range of function f (x) = - (x-1) &# + 1 is
8. The function y is equal to the range of x plus 1 / 2x plus 4
9. Let f (x) = x ^ 2-2x + 1-k ^ 2, for any x ∈ (0, positive infinity) f (x) > 2k-2, the value range of K is obtained
10. The function f (x) = x & # 178; + 2x-3a, X belongs to [- 2,2] 1, if FX + 2A ≥ 0, it holds. Find the value range of A
11. The definition field of odd function f (x) is R. when x > 0, f (x) = - x 2x2, then the expression of F on R
12. Given that the function f (x) = x + B (a is greater than 0, a is not equal to 1) satisfies f (x + y) = f (x) f (y) and f (3) = 8 to find f (x)
13. If the odd function f (x) (x is not equal to o), X belongs to (0, + 00), f (x) = X-1, then the inequality f (x-1) is satisfied
14. If the odd function y = f (x) (x ≠ 0) is x ∈ (0, + ∞), f (x) = X-1, then the value range of X satisfying the inequality f (x-1) < 0 is obtained
15. If the odd function y = f (x) (x belongs to R and X does not = 0), when x is 0 to positive infinity, f (x) = X-1, and f (x-1)
16. If the odd function y = f (x), (x is not equal to 0), if x belongs to (0, + ·), f (x) = X-1, find the inequality f (x-1)
17. It is known that the function f (x) is defined as an increasing function f (2) = 1, f (XY) = f (x) + F (y) defined on greater than 0, which solves the inequality f (4) f (X-2) less than or equal to 3
18. If x is greater than 0, f (x) is greater than 1, f (a + b) = f (a). F (b) It is proved that FX is a proper function on R, a and B belong to R Increasing function
19. Given that f (x) is defined as R, for any x, y belongs to R, f (x + y) + F (X-Y) = 2F (x) (y), and f (0) is not equal to 0 If there is a constant C, Let f (C / 2) = 0. Proof: for any x belonging to R, f (x + C) = - f (x)
20. It is known that the function f (x) is defined on R, for any x, y belongs to R, f (x + y) + F (X-Y) = 2F (x) f (y), and f (0) is not equal to 0 1, prove that f (0) = 1.2, y = f (x) is even function