Question

The set of all values of x for which $f(x) = ||x|-1|$ is differentiable is

• A. $\{-1,1\}$
• B. $\mathbb{R} - \{-1,1,0\}$
• C. $\mathbb{R}$
• D. $(0, \infty)$

Hint:

To find the points where a function with nested absolute values like $f(x) = |g(|h(x)|)|$ is not differentiable, you must check all points where the arguments of any of the absolute value functions become zero. In this case, check where $h(x)=0$ and where $g(|h(x)|)=0$.

Answer 1

The Correct Option is B