question_answer

If\[f(x)=\left\{ \begin{align}   & \frac{|x-a|}{x-a},\text{when}\,x\ne a \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,1,\text{when}\,x=a \\ \end{align} \right.\],then                             [AI CBSE 1983]

A)            \[f(x)\]is continuous at \[x=a\]

B)            \[f(x)\]is discontinuous at \[x=a\]

C)            \[\underset{x\to a}{\mathop{\lim }}\,f(x)=1\]

D)            None of these