Q66 / 125 · BITSAT 2009 · Mathematics

The set of points of discontinuity of the function \(1 / \log |\mathrm{x}|\) is -

  • Correct answer
    A
    \(\{-1,0,1\}\)
  • B
    \(\{0\}\)
  • C
    \(\{0,1\}\)
  • D
    None of these

Solution

Let \(f(x)=\frac{1}{\log |x|}\) The points of disconinuity of \(f(x)\) are those points where \(f(x)\) is undefined or infinite. It is undefined when \(x=0\) and is infinite when \(\log |x|=0,|x|=1\), i.e. \(x= \pm 1\). \(\therefore \quad\) Set of points of discontinuity \(=\{-1,0,1\}\).

Hence, the correct answer is option: 'A'.

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