question_answer

If \[f(x)=\left\{ \begin{matrix}    \frac{[x]-1}{x-1}, & x\ne 1  \\    0, & x=1  \\ \end{matrix} \right.\]   where [  ] denotes the greatest integer function, then f(x) is _________.

A)  continuous as well as differentiable at x = 1

B)  differentiable but not continuous at x= 1

C)  continuous but not differentiable at x = 1

D)  neither continuous nor differentiable at x = 1

E)  None of these