12th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-3

  • question_answer
    If \[\mathbf{f}\left( \mathbf{x} \right)=\left\{ \begin{align}   & x,\,\mathbf{when}\text{ }\mathbf{x}\text{ }\mathbf{is}\text{ }\mathbf{rational} \\  & 1-x,\mathbf{when}\text{ }\mathbf{x}\text{ }\mathbf{is}\text{ }\mathbf{irrational} \\ \end{align} \right.\] then

    A) f(x) is continuous \[\forall x\]                      

    B) f(x) is differentiable \[\forall x\]

    C) f(x) is continuous at \[x=\frac{1}{2}\]                 

    D) f(x) is discontinuous at \[x=\frac{1}{2}\]

    Correct Answer: C

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