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

  • question_answer
    If \[f(x)=\frac{1}{1-x}\], then the points of discontinuity of the function \[f[f\{f(x)\}]\] are

    A) {0, -1}

    B) {0, 1}

    C) {1, -1}

    D) None of these

    Correct Answer: B

    Solution :

    [b] We have, \[f(x)=\frac{1}{1-x}\]. As at \[x=1,f(x)\] is not defined, \[x=1\] is a point of discontinuity of f(x). If \[x\ne 1,[f(x)]=f\left( \frac{1}{1-x} \right)=\frac{1}{1-1/(1-x)}=\frac{x-1}{x}\] \[\therefore x=0,1\] are points of discontinuity of \[f[f(x)]\]. If \[x\ne 0,x\ne 1\] \[f[f\{f(x)\}]=f\left( \frac{x-1}{x} \right)=\frac{1}{1-\frac{(x-1)}{x}}=x\]


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