If f (x) = SiNx + 2 | SiNx | (x ∈ [0,2 π)] and y = k have only two different intersections, then the value range of K is () A. [-1，1]B. （1，3）C. （-1，0）∪（0，3）D. [1，3]

If f (x) = SiNx + 2 | SiNx | (x ∈ [0,2 π)] and y = k have only two different intersections, then the value range of K is () A. [-1，1]B. （1，3）C. （-1，0）∪（0，3）D. [1，3]

According to the problem, f (x) = SiNx + 2 | SiNx | (x ∈ [0, 2 π) = 3sinx, X ∈ [0, π) − SiNx, X ∈ [π, 2 π], draw the function image in the coordinate system: from the image, when the line y = k, K ∈ (1, 3), the image of F (x) = SiNx + 2 | SiNx |, X ∈ [0, 2 π] and the line y = k have and only have two different intersections

If f (x) = SiNx + 2 | SiNx | (x ∈ [0,2 π)] and y = k have only two different intersections, then the value range of K is ()
A. [-1，1]B. （1，3）C. （-1，0）∪（0，3）D. [1，3]

According to the problem, f (x) = SiNx + 2 | SiNx | (x ∈ [0, 2 π) = 3sinx, X ∈ [0, π) − SiNx, X ∈ [π, 2 π], draw the function image in the coordinate system: from the image, when the line y = k, K ∈ (1, 3), the image of F (x) = SiNx + 2 | SiNx |, X ∈ [0, 2 π] and the line y = k have and only have two different intersections

If f (x) = SiNx + 2 | SiNx | (x ∈ [0,2 π)] and y = k have only two different intersections, then the value range of K is ()
A. [-1，1]B. （1，3）C. （-1，0）∪（0，3）D. [1，3]

According to the problem, f (x) = SiNx + 2 | SiNx | (x ∈ [0, 2 π) = 3sinx, X ∈ [0, π) − SiNx, X ∈ [π, 2 π], draw the function image in the coordinate system: from the image, when the line y = k, K ∈ (1, 3), the image of F (x) = SiNx + 2 | SiNx |, X ∈ [0, 2 π] and the line y = k have and only have two different intersections

If f (x) = cosx + | SiNx | (x ∈ [0, 2 π]) and the line y = k have only four different intersections, then the value range of K is______ ．

When x ∈ [0, π], | SiNx | = SiNx, so y = SiNx + cosx = 2Sin (x + π 4), when x ∈ (π, 2 π), | SiNx | = - SiNx, so y = - SiNx + cosx = 2Sin (π 4-x), draw the image of piecewise function according to the analytic formula, as shown in the figure: according to the image, the range of K is: 1 ≤ K < 2. So the answer is: 1 ≤ K < 2