JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    If the function \[f(x)=\,\left\{ \begin{matrix}    5x-4 & , & \text{if} & 0<x\le 1  \\    4{{x}^{2}}+3bx & , & \text{if} & 1<x<2  \\ \end{matrix} \right.\] is continuous at every point of its domain, then the value of b is                    [RPET 2000]

    A)            ? 1

    B)            0

    C)            1

    D)            None of these

    Correct Answer: A

    Solution :

               \[f(x)\] is continuous at every point of its domain,            Þ\[\underset{x\to {{1}^{-}}}{\mathop{\lim }}\,f(x)=\underset{x\to {{1}^{+}}}{\mathop{\lim }}\,f(x)=f(1)\]            Þ \[5\times 1-4=4\times 1+3\times b\times 1\]            Þ \[1=4+3b\]  Þ  \[3b=-3\] Þ \[b=-1\].


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