Given that the function f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = - f (x). When x belongs to [0,2], f (x) = 3x + 2, then the analytic expression of the function in the interval [- 4,0] is?

Given that the function f (x) is an even function defined on R, and for any x belonging to R, f (2 + x) = - f (x). When x belongs to [0,2], f (x) = 3x + 2, then the analytic expression of the function in the interval [- 4,0] is?

Pro, this problem is done, but I am not sure right or wrong (but theoretically, it should be done), so for reference only, because f (2 + x) = - f (x) in X take any real number, so, X can also take [0,2]. Also because it is even function, so f (x) = f (- x). That is - f (x) = 3x + 2. F (2 + x) = 3