Let f be the function on [0, 1] defined by

\(f(x)=\left\{\begin{array}{ccc} (-1)^r, & \text { if } \frac{1}{r+1} \leq x<\frac{1}{r}, & r=1,2,3 \ldots \ldots \\ 0, & \text { if } & x=0 \\ 1, & \text { if } & x=1 \end{array}\right.\) then which of the following is/are) correct:

(A). f(x) is continuous at x = 1/2

(B). f(x) is continuous on [0, 1]. 

(C). f(x) is discontinuous at 1/2.

(D). f(x) is continuous on (1/2, 1)

Choose the correct answer from the options given below: