Question

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

• A. $1$
• B. $2$
• C. $3$
• D. $4$
• E. Infinitely many

Answer 1

The correct option is C $3$

At $x=0,\pm 1$, the function is discontinuous.
At $x=0,{\log }_e\left|x\right|$ is not defined.
At $x=1$ and $-1,{\log }_e\left|x\right|$ is $0$, hence $f\left(x\right)=\infty$
So, $x=0,\pm 1$ are the points of discontinuity.