JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    Function \[f(x)=\left\{ \begin{align}   & \,\,\,x-1,\ x<2 \\  & 2x-3,\,x\ge 2 \\ \end{align} \right.\]is  a continuous function [MP PET 1996]

    A)            For all real values of x              

    B)            For \[x=2\]only

    C)            For all real values of x such that \[x\ne 2\]

    D)            For all integral values of x only

    Correct Answer: A

    Solution :

               Since \[\underset{x\to 2-}{\mathop{\lim }}\,f(x)=\underset{x\to 2+}{\mathop{\lim }}\,f(x)=f(2)=1\]                    Also it is continuous for all values of x, less than 2 and greater than 2.


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