Let f(x) = cos^{-1} (cos2x) and g(x) = |cos x| then

(A) number of solution of f(x) = g(x) in [0,2π] is 4.

(B) max {f(x), g(x)} is a periodic function

(C) max {f(x), g(x)} is a non differentiable function for some x,

(D) min {f(x), g(x)} is an even function