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JEE Main & Advanced Sample Paper JEE Main Sample Paper-3

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

    A)  2                            

    B)  1

    C)  0                            

    D)  infinite

    Correct Answer: A

    Solution :

     \[f\{f[fx]\}=f\left[ f\left( \frac{1}{1-x} \right) \right]=f\left( \frac{1}{1-\frac{1}{1-x}} \right)\] \[=f\left( \frac{x-1}{x} \right)\] \[\therefore \]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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