Question

Determine the number of points where the function

$f\left(x\right)=\frac{1}{\log \left|x\right|}$ is discontinuous

Answer 1

The function is not defined for $x=0$ and hence it is a point of discontinuity. Further if $\log \left|x\right|=0$ or $\left|x\right|=1orx=\pm 1$ then also function is not defined.
Hence it has three points of discontinuity at $x=0,1,-1.$
Ans: 3