It is known that the function f (x) defined on the real number set R satisfies the following conditions: (1) f (- x) = f (x) (2) f (2 + x) = f (2-x) (3) when x ∈ [0,2], the analytic formula y = 2x-1, and the analytic formula on X ∈ [- 4,0] is obtained

It is known that the function f (x) defined on the real number set R satisfies the following conditions: (1) f (- x) = f (x) (2) f (2 + x) = f (2-x) (3) when x ∈ [0,2], the analytic formula y = 2x-1, and the analytic formula on X ∈ [- 4,0] is obtained

Because f (- x) = f (x)
So the function f (x) is even and its image is symmetric about the Y axis
And f (2 + x) = f (2-x)
So f (4 + x) = f (- x) = f (x)
So the function f (x) is a periodic function with the minimum positive period of 4
Because when x ∈ [0,2], the analytic formula y = 2x-1
Therefore, according to the image, when x ∈ [- 4, - 2], it is also a linear function, which can be set as y = ax + B, and when x = - 4, y = - 1
When x = - 2, y = 3
The solution is a = 2, B = 7, that is, when x ∈ [- 4, - 2], y = 2x + 7
When x ∈ [- 2,0], it is also a linear function, which can be set as y = ax + B
And when x = - 2, y = 3, when x = 0, y = - 1
The solution is a = - 2, B = - 1, that is, when x ∈ [- 2,0], y = - 2x-1
To sum up, when x ∈ [- 4, - 2], y = 2x + 7
When x ∈ [- 2,0], y = - 2x-1