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JEE Main & Advanced Sample Paper JEE Main Sample Paper-36

  • question_answer
    If\[f(x)=\frac{1}{1-x}\], the number of points of discontinuity of\[f\{f[f(x)]\}\]is:

    A) \[2\]                             

    B) \[1\]

    C) \[0\]                             

    D)  infinite

    Correct Answer: A

    Solution :

    \[f\{f[f(x)]\}=f\left[ f\left( \frac{1}{1-x} \right) \right]=f\left( \frac{1}{1-\frac{1}{1-x}} \right)=f\left( \frac{x-1}{x} \right)\]\[\therefore \]\[f(x)\]is not defined for\[x=1;\,\,f\left( \frac{1}{1-x} \right)\]is not defined for\[x=0\]. \[\therefore \]\[f\{f[f(x)]\}\]is discontinuous at \[x=0\] and 1 \[i.e.,\]there are two points of discontinuity.


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