![](data:image/svg+xml;utf8,<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 72 71" width="72"></svg>)
Given that F & nbsp; (x + 1) is odd, F & nbsp; (x-1) is even, and F & nbsp; (0) = 2, then f & nbsp; (2012) = () A. -2B. 0C. 2D. 3
Because the function f (x + 1) is an odd function, if f (x + 1) = - f (- x + 1) let t = x + 1, then f (T) = - f (2-T) ∵ if f (x-1) is an even function ∵ f (x-1) = f (- x-1), let X-1 = t, then f (T) = f (- T-2) ∵ f (- T-2) = - f (- t + 2) let - T-2 = m, then f (m) = - f (...)
RELATED INFORMATIONS
- 1. Given the function f (x) = (radical 3) sin2x + cos2x, if f (x-a) is even, then a value of a is
- 2. Let f (x) = asin (Wx + phi) (a ≠ 0, w > 0, Phi > 0, │ phi │ 0, Phi > 0, │ phi │
- 3. Function judging parity Y = half plus the reciprocal of the x power of a, judge the parity, folks!
- 4. The domain of y = LG (cosx SiNx)
- 5. Given f (x) = {(6-A) x-4a, x = 1}
- 6. The sum of three consecutive natural numbers is less than 15. How many natural arrays are there in total? Write them separately
- 7. The sum of three consecutive natural numbers is less than 15. Please write out how many groups there are in such a natural array
- 8. The sum of three consecutive natural numbers is less than 15. There are several groups in such an array
- 9. The sum of three consecutive natural numbers is less than 11. Such a natural array has () A. Group 1 B. group 2 C. group 3 d. group 4
- 10. It is known that a and B are real numbers, and e < a < B, where e is the base of natural logarithm
- 11. Y = f (x) is an even function defined on R, The image is symmetric with respect to x = 1. For any x 1, x 2 belongs to [0,1 / 2], and f (x 1 + x 2) = f (x 1) * f (x 2), and f (1) = a > 0 1. Find f (1 / 2) and f (1 / 4) 2. Prove that f (x) is a periodic function
- 12. If f (x) is odd, G (x) is even, and f (x) - G (x) = x2 + 2x + 3, then f (x) + G (x)= It's the square of x plus 2x + 3
- 13. If f (x) is a function x (R) = 0, and f (x / R) = 0, then f (f) is a function x (R) = 0, F (101 / 17), f (106 / 15),
- 14. It is known that the derivative of y = f (x) defined on R is f '(x), satisfying f' (x)
- 15. The differentiable function f (x) defined on R is known, which satisfies f '(x)
- 16. The problem of function image, the problem of function image symmetry, please write the proof in detail, 1. What is the symmetry between the image of function y = f (x-1) and the image of function y = f (1-x) 2. What is the symmetry between the image of function y = - f (x-1) and the image of function y = f (1-x) The first one I think is about x = 1 symmetry. I got it by enumerating. I made f (x) = x, X & # 178;, 1 / X try to get it. I know how to prove it first Second, I gave some examples, but I didn't get them. I also want to prove them
- 17. If a function has two symmetries, it must be periodic. Why
- 18. LG25 + LG2 * LG50 + (LG2) ^ 2 after (LG2) ^ 2. How can the ^ 2 after (LG2) ^ 2 disappear in the next step? Where?
- 19. Calculation: (1) LG25 + lg2lg50 + (LG2) 2 (2) 813 + (12) − 2 + (27-1 + 16-2) 0 + 416
- 20. Let LG2 = a, Lg3 = B. use a, B to express LG10 (senior one mathematics)