Q. If $f(x) = |\log{|x|}|$, then
A) $f(x)$ is continuous and differentiable for all $x$ in its domain
B) $f(x)$ is continuous for all $x$ in its domain but not differentiable at $x = \pm 1$
C) $f(x)$ is neither continuous nor differentiable at $x = \pm 1$
D) None of the above
Explanation
(b)
[image:5_image7.emf]
From the graph of $f(x) = |\log{|x||}$ it is clear that $f(x)$ is everywhere continuous but not differentiable at $x = \pm 1$, due to sharp edge
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.