Question

If $f\left(x\right)=\left|\log \left|x\right|\right|$, then

• A. $f\left(x\right)$ is continuous and differentiable for all $x$ in its domain
• B. $f\left(x\right)$ is continuous for all $x$ in its domain but not differentiable at $x=\pm 1$
• C. $f\left(x\right)$ is neither continuous nor differentiable at $x=\pm 1$
• D. None of the above

Answer 1

The correct option is B $f\left(x\right)$ is continuous for all $x$ in its domain but not differentiable at $x=\pm 1$

It is evident from the graph of $f\left(x\right)=\left|\log \left|x\right|\right|$ that $f\left(x\right)$ is everywhere continuous but not differentiable at $x=\pm 1$