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 follow these steps:

### 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 is defined for positive arguments. Therefore, we need \( |x| > 0 \), which means \( x \neq 0 \).

**Domain:** The domain of \( f(x) \) is all real numbers except \( x = 0 \), i.e., \( (-\infty, 0) \cup (0, \infty) \).

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