Discuss the continuity and differentiability of `f(x)=|log|x||` .

Explanation

To discuss the continuity and differentiability of the function \( f(x) = |\log|x|| \), we will analyze the function step by step.

### Step 1: Determine the domain of \( f(x) \)

The function \( f(x) = |\log|x|| \) involves the logarithm of the absolute value of \( x \). The logarithm function \( \log(x) \) is defined for \( x > 0 \). Therefore, \( \log|x| \) is defined for all \( x \neq 0 \).

Thus, the domain of \( f(x) \) is:
\[
...