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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    The function 'f' is defined by \[f(x)=2x-1,\]if \[x>2\], \[f(x)=k\ \]if\[x=2\]and \[{{x}^{2}}-1,\]if \[x<2\]is continuous, then the value of k is equal to [Pb. CET 2002]

    A)            2

    B)            3

    C)            4

    D)            ?3

    Correct Answer: B

    Solution :

               We have \[f(x)=2x-1,\]if \[x>2,\] \[f(x)=k,\]                    If \[x=2\] and \[{{x}^{2}}-1,\] if \[x<2\], function is continuous.                    \ \[\underset{x\to 2}{\mathop{\lim }}\,f(x)=f(2)\]Þ \[\underset{x\to 2}{\mathop{\lim }}\,(2x-1)=k\Rightarrow k=3\].


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