It is known that f (x) is a function defined on R. for any x belonging to R, f (x + 4) = f (x) + 2F (2), if the image of function f (x-1) is symmetric with respect to x = 1 And f (1) = 2, find f (2011) =?

It is known that f (x) is a function defined on R. for any x belonging to R, f (x + 4) = f (x) + 2F (2), if the image of function f (x-1) is symmetric with respect to x = 1 And f (1) = 2, find f (2011) =?

The image of F (x-1) is symmetric with respect to x = 1, then the image of F (x) is symmetric with respect to x = 2, f (x + 4) = f (x) + 2F (2) let x = 0f (4) = f (0) + 2F (2) and ∵ the image of F (x) be symmetric with respect to x = 2 ∵ f (4) = f (0) ∵ 2F (2) = 0 ∵ f (2) = 0 ∵ f (x + 4) = f (x) f (2011) = f (2007 + 4) = f (2007) = f (2003) =... = f (3) = f (2 * 2 -