**Question:**

The set of points at which the function $f(x)=\frac{1}{\log |x|}$ is not differentiable, is_____________

**Solution:**

The given function is $f(x)=\frac{1}{\log |x|}$.

For $f(x)$ to be defined,

$x \neq 0$ and $\log |x| \neq 0$

$\Rightarrow x \neq 0$ and $|x| \neq 1$

$\Rightarrow x \neq 0$ and $x \neq \pm 1$

Thus, the function *f*(*x*) is not defined when *x* = −1, *x* = 0 and *x* = 1

We know that, the logarithmic function is differentiable at each point in its domain. Every constant function is differentiable at each *x* ∈ R. Also, the quotient of two differentiable functions is differentiable.

So, the function $f(x)=\frac{1}{\log |x|}$ is not differentiable at $x=-1, x=0$ and $x=1$.

Thus, the set of points at which the function $f(x)=\frac{1}{\log |x|}$ is not differentiable is $\{-1,0,1\}$

The set of points at which the function $f(x)=\frac{1}{\log |x|}$ is not differentiable, is $\{\underline{-1}, \underline{0}, 1\}$