Question

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

Answer 1

Given that,

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

for the function to be defined denominator $\ne$0.

$i.e.,log|x|\ne 0$

$i.e.,|x|\ne 0$

$x\ne \pm 1$

also the function $log|x|$ is not defined for x=0.

$\therefore$ The points of discontinuities are $0,\pm 1$ and their number is 3.