question_answer

If \[f(x)=\left\{ \begin{align}   & x-1,\,\,\,x<0 \\  & \,\,\,\,\,\,\frac{1}{4},\,\,x=0 \\  & \,\,\,\,\,\,\,{{x}^{2}},\,\,x>0 \\ \end{align} \right.\], then [Roorkee 1988]

A)            \[\underset{x\to 0+}{\mathop{\lim }}\,f(x)=1\]

B)            \[\underset{x\to 0-}{\mathop{\lim }}\,f(x)=1\]

C)            \[f(x)\]is discontinuous at\[x=0\]    

D)            None of these

Correct Answer: C

Solution :

           Clearly from curve drawn of the given function \[f(x)\] is discontinuous at \[x=0.\]