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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    The function \[f(x)\,=\left\{ \begin{align}   & x+2\,\,\,\,,\,\,\,1\le x\le 2 \\  & 4\,\,\,\,\,\,\,\,\,\,\,,\,\,\,x=2 \\  & 3x-2\,\,,\,\,\,x>2 \\ \end{align} \right.\] is continuous at [DCE 1999]

    A)            \[x=2\] only

    B)            \[x\le 2\]

    C)            \[x\ge 2\]

    D)            None of these

    Correct Answer: C

    Solution :

               Clearly the function is defined only in the interval \[[1,\,\infty )\] hence option  cannot even apply. For \[x>2,\,y=3x-2\] which is a straight line, hence continuous. Further \[y=4\] at \[x=2\]. Hence, the function is continuous at \[x=2\] also (but not at \[x=2\] only).


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