Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$

Answer 1

Answer: (C)

$3$

The function $\log |x|$ is not defined at $x=0$.

So, $x=0$ is a point of discontinuity.

Also for $f\left(x\right)$ to be defined, $x\log |x|\ne 0\Rightarrow x\ne x\pm 1$.

Hence, $0,1,-1$ are three points of discontinuity.