Question

If $f\left(x\right)=|x^2+(k-1\left)\right|x|-k|$ is non differentiable at five real points, then k will lie in

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

Answer 1

The correct option is C

$(-\infty ,0)-\{-1\}$

$f\left(x\right)=|x^2+(k-1\left)\right|x|-k|=\left|(|x|+k)\right|(|x|-1)$

Both roots of $(x-1)(x+k)=0$ should be positive and distinct

$\Rightarrow k\in (-\infty ,0)-\{-1\}$