Let y = f (x) be an even function defined on R, and its image is symmetric with respect to x = 2. When x ∈ [- 2,2] is known, the function f (x) = - x ^ 2 + 1, then when x ∈ [- 6, - 2], f (x)=

Let y = f (x) be an even function defined on R, and its image is symmetric with respect to x = 2. When x ∈ [- 2,2] is known, the function f (x) = - x ^ 2 + 1, then when x ∈ [- 6, - 2], f (x)=

If f (x) = f (- x), then f (x) = f (4-x), so f (4-x) = f (- x), that is, f (x + 4) = f (x)
So for X ∈ [- 6, - 2], f (x) = f (x-4) = (x-4) ^ 2 + 1 = x ^ 2-8x + 17