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Q.

Let [x] denote the greatest integer function, and let m and n respectively be the numbers of the points, where the function $f (x) = [x] + | x - 2 |, - 2 < x < 3,$ is not continuous and not differentiable. Then $m + n$ is equal to:

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a

8

b

7

c

6

d

9

answer is C.

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Detailed Solution

$f (x) = [x] + | x - 2 | - 2 < x < 3$
$f (x) = \{\begin{array}{cc} - x, & - 2 < x < - 1 \\ - x + 1, & - 1 \leq x < 0 \\ - x + 2, & 0 \leq x < 1 \\ - x + 3, & 1 \leq x < 2 \\ x, & 2 \leq x < 3 \end{array}$
So f(x) is not continuous at 4 points and not differentiable at 4 point
So m + n = 4 + 4 = 8

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