Functions Question 378
Question: $ f(x)=| | x |-1 | $ is not differentiable at
[IIT Screening 2005]
Options:
A) 0
B) $ \pm 1,0 $
C) 1
D) $ \pm 1 $
Show Answer
Answer:
Correct Answer: B
Solution:
$ = \begin{cases} & |x|-1,,|x|-1\ge 0 \\ & -|x|+1,,|x|-1<0 \\ \end{cases} . $ $ = \begin{cases} & |x|-1,,x\le -1or,x\ge 1 \\ & -|x|+1,,-1<x<1 \\ \end{cases} . $ $ = \begin{cases} & -x-1,,x\le -1 \\ & x+1,-1<x<0 \\ & -x+1,,0\le x<1 \\ & x-1,,x\ge 1 \\ \end{cases} . $ From the graph. It is clear that $ f(x) $ is not differentiable at $ x=-1,,0 $ and 1.
BETA
