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JEE Main & Advanced Mathematics Limits, Continuity and Differentiability Question Bank Self Evaluation Test - Continuity and Differentiability

  • question_answer
    If function \[\text{f(x)=}\left\{ \begin{align}   & \text{x,if}\,\,\text{x}\,\,\text{is}\,\,\text{rational} \\  & \text{1-x,if}\,\,\text{x}\,\,\text{is}\,\,\text{irrational} \\ \end{align} \right.\text{,then}\] the number of points at which f(x) is continuous, is-

    A) \[\infty \]

    B)  1

    C) 0

    D) None of these

    Correct Answer: B

    Solution :

    [b] Let \[x=a\in Q;f(a)=a\] \[f({{a}^{+}})=1-a\] or \[a;f({{a}^{-}})=1-a\,\,or\,\,a\] continuous at where \[1-a=a\Rightarrow a=1/2\] \[\Rightarrow \] continuous at one point.


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