Question

The number of points at which $f\left(x\right)=\frac{1}{\log |x|}$ is discontinuous is

Answer 1

$f\left(x\right)=\frac{1}{\log |x|}$
Since, $\log x$ is defined for $x>0$
So, for $f\left(x\right)$ to be defined
$\log |x|\ne 0$
So,$f\left(x\right)$ is not defined at $x=-1,0$ and $1$ and it is continuous at every real number.
Hence, there are $3$ points of discontinuity