Question

The set of points at which the function $f\left(x\right)=\frac{1}{\log \left|x\right|}$ is not continuous, is ___________.

Answer 1

The given function $f\left(x\right)=\frac{1}{\log \left|x\right|}$ is discontinuous when $\log \left|x\right|=0$.

Also, x ≠ 0 (log 0 is not defined)

Now,

$\log \left|x\right|=0$

$\Rightarrow \left|x\right|=1$

$\Rightarrow x=\pm 1$

Thus, the given function is not continuous at x = 0, x = −1 and x = 1.

Hence, the set of points at which the given function is not continuous is {−1, 0, 1}.


The set of points at which the function $f\left(x\right)=\frac{1}{\log \left|x\right|}$ is not continuous, is ___{−1, 0, 1}___.