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(D) The function is defined as $f(x) = [x] + |1 - x|$ on the interval $[-1, 3]$.Points of discontinuity for the greatest integer function $[x]$ in the

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$4$

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(D) The function is defined as $f(x) = [x] + |1 - x|$ on the interval $[-1, 3]$.Points of discontinuity for the greatest integer function $[x]$ in the interval $[-1, 3]$ are $x = 0, 1, 2, 3$.At $x = 1$,the function is $f(x) = [x] + |1 - x|$. Since $|1 - x|$ is continuous everywhere,the non-differentiability arises from the jump discontinuities of $[x]$ at $x = 0, 1, 2, 3$ and the corner point of $|1 - x|$ at $x = 1$.Checking the points:$1$. At $x = 0$: $[x]$ is discontinuous,so $f(x)$ is not differentiable.$2$. At $x = 1$: $[x]$ is discontinuous and $|1 - x|$ has a corner,so $f(x)$ is not differentiable.$3$. At $x = 2$: $[x]$ is discontinuous,so $f(x)$ is not differentiable.$4$. At $x = 3$: $[x]$ is discontinuous,so $f(x)$ is not differentiable.Thus,the function is not differentiable at $x = 0, 1, 2, 3$. There are $4$ such points.

Let $[x]$ denote the greatest integer less than or equal to $x$. Then the number of points where the function $y = [x] + |1 - x|$ for $-1 \leq x \leq 3$ is not differentiable,is

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