We know that the function f (x) satisfies the following conditions: ① the domain of definition is R; ② ∀ x ∈ R, f (x + 2) = 2F (x); ③ when x ∈ [0, 2], f (x) = 2 - | 2x-2 |. Note that φ (x) = f (x) − | x | (x ∈ [− 8, 8]). According to the above information, we can get that the number of zeros of function φ (x) is () A. 15B. 10C. 9D. 8

We know that the function f (x) satisfies the following conditions: ① the domain of definition is R; ② ∀ x ∈ R, f (x + 2) = 2F (x); ③ when x ∈ [0, 2], f (x) = 2 - | 2x-2 |. Note that φ (x) = f (x) − | x | (x ∈ [− 8, 8]). According to the above information, we can get that the number of zeros of function φ (x) is () A. 15B. 10C. 9D. 8

According to the meaning of the problem, we can draw an image of the function y = f (x) (- 8 ≤ x ≤ 8): & nbsp; in the same coordinate system, we can draw an image of G (x) = | x | (x ∈ [- 8,8]), and we can get that two images have eight intersections on the right side of the X axis. Therefore, φ (x) = f (x) − x | (x ∈ [- 8,8]) has eight zeros, ∵ any x, and f (x + 2) = 2F (...)

If the definition field of function y = f (x) is [0,1], then function f (x) = f (x + a) + 2F (2x + a) (0

x+a [0,1]
2x+a [0,1]
-1

When x ∈ (1,2], f (x) = 2-x, if y = f (x) - K (x-1) has three zeros, then the value range of real number k is

If x ∈ (1,2], f (x) = 2 / 2 ∈ (1,2], f (x) = 2F (x) = 2 (2-x / 2) = 4-x, similarly, if x ∈ (2 ^ m, 2 ^ (M + 1)], m ∈ n, then x / 2 ^ m ∈ (1,2], f (x) = 2 ^ m * f (x / 2 ^ m) = 2 ^ m * (2-x / 2 ^ m) = 2 ^ (M +...)

If the function f (x) whose domain is r satisfies f (x) + 2F (- x) = 2x + 1, then f (x) = ()
A. -2x+1B. 2x-13C. 2x-1D. -2x+13

∵ f (x) + 2F (- x) = 2x + 1, ①, let x = - x, then f (- x) + 2F (x) = - 2x + 1, ②, ② × 2 - ①, 3f (x) = - 6x + 1, ∵ f (x) = - 2x + 13, so choose: D