The set of points where the function f(x)=[x]+|1−x|,−1≤x≤3where [.]  denotes the greatest integer function, is not differentiable, is

# The set of points where the function $f\left(x\right)=\left[x\right]+|1-x|,-1\le x\le 3$where denotes the greatest integer function, is not differentiable, is

1. A

$\left\{-1,0,1,2,3\right\}$

2. B

$\left\{-1,0,2\right\}$

3. C

$\left\{0,1,2,3,\right\}$

4. D

$\left\{-1,0,1,2\right\}$

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### Solution:

We have

$f\left(x\right)=\left\{\begin{array}{l}-x, -1\le x<0\\ 1-x, 0\le x<1\\ x, 1\le x<2\\ 1+x, 2\le x<3\\ 5, x=3\end{array}\right\$

Clearly, is discontinuous at

So, it is not differentiable at these points.

At $x=-1$, we have

$\underset{x\to -{1}^{+}}{lim} f\left(x\right)=\underset{x\to -{1}^{+}}{lim} -x=1=f\left(-1\right)$

So, it is continuous at $x=-1$.

Also, (RHD at $x=-1\right)=-1$ (a finite number).

Therefore,  is differentiable at

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