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JEE Main & Advanced Sample Paper JEE Main - Mock Test - 34

  • question_answer
    If \[f(x)=\left\{ \begin{align}   & [x]+[-x];x\ne 2 \\  & \lambda \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,;\,x=2 \\ \end{align} \right.\] then f is continuous at x = 2, provided A. is equal to -

    A) 1    

    B)                   0     

    C) -1                    

    D)        2

    Correct Answer: B

    Solution :

    [c] \[\because f\left( x \right)\]is continuous at x = 2 \[\therefore f(2)=\underset{x\to 2}{\mathop{lim}}\,f(x)\] \[\Rightarrow \lambda =\underset{x\to 2}{\mathop{lim}}\,[x]+[-x]\] \[\lambda =-1\] \[\left\{ \begin{align}   & \because we\text{ }know\left[ x \right]+\left[ -x \right]=0:x\in I \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,-1:x\notin I \\ \end{align} \right.\]


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