MCQ
The function given by $y = | |x| - 1|$ is differentiable for all real numbers except the points
- ✓$\{0, 1, -1\}$
- B$ \pm 1$
- C$1$
- D$-1$
✓
Answer
Correct option: A.
$\{0, 1, -1\}$
a
$f(x)=|| x|-1|$ is non-differentiable when $|x|=0$ and when $|x|-1=\theta$ or $x=0$ and $\mathrm{x}=\pm 1.$
$f(x)=|| x|-1|$ is non-differentiable when $|x|=0$ and when $|x|-1=\theta$ or $x=0$ and $\mathrm{x}=\pm 1.$
Alternative method:
The graph of $y=|| x|-1|$ is as follows:
It has sharp turn at $x=-1,0$ and $1$ and hence, is not differentiable at $x=-1,0,1.$
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