question_answer

If \[\mathbf{f}\left( \mathbf{x} \right)=\left\{ \begin{align}   & x,\,\mathbf{when}\text{ }\mathbf{x}\text{ }\mathbf{is}\text{ }\mathbf{rational} \\  & 1-x,\mathbf{when}\text{ }\mathbf{x}\text{ }\mathbf{is}\text{ }\mathbf{irrational} \\ \end{align} \right.\] then

A) f(x) is continuous \[\forall x\]                      

B) f(x) is differentiable \[\forall x\]

C) f(x) is continuous at \[x=\frac{1}{2}\]                 

D) f(x) is discontinuous at \[x=\frac{1}{2}\]