If f (x) is an even function defined on R with period of 3 and f (2) = 0, then the minimum number of solutions of the equation f (x) = 0 in the interval (0,6) is () A. 5B. 4C. 3D. 2

If f (x) is an even function defined on R with period of 3 and f (2) = 0, then the minimum number of solutions of the equation f (x) = 0 in the interval (0,6) is () A. 5B. 4C. 3D. 2

∵ f (x) is an even function defined on R, and the period is 3, f (2) = 0, ∵ f (- 2) = 0, ∵ f (5) = f (2) = 0, f (1) = f (- 2) = 0, f (4) = f (1) = 0. In the interval (0, 6), f (2) = 0, f (5) = 0, f (1) = 0, f (4) = 0

It is known that for any real number x, the function f (x) satisfies f (- x) = f (x). If the equation f (x) = 0 has 2009 real solutions, then the sum of these 2009 real solutions is______ ．

Let f (x) = 0 be the real solution of x1, X2 , X2009, let x1 ＜ x2 ＜ If there is x0 such that f (x0) = 0, then f (- x0) = 0, ｜ X1 + X2009 = 0, X2 + x2008 = 0 ，x1004+x1006=0，x1005=0，∴x1+x2+… +So the answer is: 0

It is known that the function f (x) whose domain is r decreases monotonically in the interval (- ∞, 5). For any real number T, f (5 + T) = f (5-T), then the following formula must be true ()
A. f（-1）＜f（9）＜f（13）B. f（13）＜f（9）＜f（-1）C. f（9）＜f（-1）＜f（13）D. f（13）＜f（-1）＜f（9）

The image of ∵ f (5 + T) = f (5-T) ∵ function f (x) is symmetric with respect to x = 5 ∵ f (- 1) = f (11), ∵ function f (x) decreases monotonically in the interval (- ∞, 5), and ∵ function f (x) increases monotonically in the interval ((∞, 5), + ∞)