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

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{- 1, 0, 1, 2, 3}

{- 1, 0, 2}

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detailed solution

Correct option is C

We have

$f (x) = \{\begin{cases} - x, - 1 \leq x < 0 \\ 1 - x, 0 \leq x < 1 \\ x, 1 \leq x < 2 \\ 1 + x, 2 \leq x < 3 \\ 5, x = 3 \end{cases}$

Clearly, $f (x)$ is discontinuous at $x = 0, 1, 2, a n d 3 .$

So, it is not differentiable at these points.

At $x = - 1$ , we have

$lim_{x \to - 1^{+}} f (x) = lim_{x \to - 1^{+}} - x = 1 = f (- 1)$

So, it is continuous at $x = - 1$ .

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

Therefore, $f (x)$ is differentiable at $x = - 1 .$

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