Let \( [x] \) denote the greatest integer function and \( f(x)= \) \( \max \{1+x+[x], 2+x, x+2[x....

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Let \( [x] \) denote the greatest integer function and \( f(x)= \)
P
\( \max \{1+x+[x], 2+x, x+2[x]\}, 0 \leq x \leq 2 \). Let \( m \)
W
be the number of
Points in \( [0,2] \), where \( f \) is not continuous and \( n \) be the number of points in \( (0,2) \), where \( f \) is not differentiable. Then \( (m+n)^{2}+2 \) is equal to:
(1) 3
(2) 6
(3) 2
(4) 11


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