Q61 / 125 · BITSAT 2016 · Mathematics

The number of points at which the function $\mathrm{f}(\mathrm{x})=\frac{1}{\log |\mathrm{x}|}$ is discontinuous is:

  • A
    1
  • B
    2
  • Correct answer
    C
    3
  • D
    4

Solution

The function $\log |x|$ is not defined at $x=0$, so, $\mathrm{x}=0$ is a point of discontinuity. Also for $\mathrm{f}(\mathrm{x})$ to be defined, $\log |\mathrm{x}| \neq 0 \Rightarrow \mathrm{x} \neq\pm 1$ Hence, 0,1,-1 are three points of discontinuity.

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

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