On the mathematical problems of periodic function Given that the even function f (x) defined on R satisfies f (x) = - f (4-x) and when x ∈ [2.4], f (x) = log2 (x-1) [2 is the base, X-1 is the real number], what is the value of F (2010) + F (2011)? By the way, since he said f (x) is an even function, is there f (4-x) = f (x-4) and why?

On the mathematical problems of periodic function Given that the even function f (x) defined on R satisfies f (x) = - f (4-x) and when x ∈ [2.4], f (x) = log2 (x-1) [2 is the base, X-1 is the real number], what is the value of F (2010) + F (2011)? By the way, since he said f (x) is an even function, is there f (4-x) = f (x-4) and why?

So f (2010) = f (251 * 8 + 2) = f (2) = log2 (1) = 0, f (2011) = f (251 * 8 + 3) = f (3) = log2 (2) = 1. Even function f (2010) + F (2011) = 1