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JEE Main & Advanced Mathematics Functions Question Bank Continuity

  • question_answer
    Let \[f(x)=\left\{ \begin{align}   & \frac{{{x}^{4}}-5{{x}^{2}}+4}{|(x-1)(x-2)|},\ \ x\ne 1,\ 2 \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,6,\,\,\,x=1 \\  & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,12,\,\,\,x=2 \\ \end{align} \right.\] Then \[f(x)\]is continuous on the set

    A)            R

    B)            \[R-\{1\}\]

    C)            \[R-\{2\}\]

    D)            \[f:R\to R\]

    Correct Answer: D

    Solution :

               For any \[x\ne 1,\,\,2\]we find that \[f(x)\] is the quotient of two polynomials and a polynomial is everywhere continuous. Therefore \[f(x)\] is continuous for all \[x\ne 1,\,\,2.\] Check continuity at \[x=1,\,\,2.\]


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