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Let \(f:(-2,2)\to R\) be defined by \[ f(x)=\begin{cases} x[x], & -2<x<0\\ (x-1)[x], & 0\le x<2 \end{cases} \] Where \([x]\) denotes the greatest integer function. If m and n respectively are the number of points in \((-2,2)\) at which \(f(x)\) is not continuous and not differentiable, then m + n is equal to _______.
- 04.00
- 04.00
- 04.00
- 04.00
Correct answer: 04.00
Solution
The function is defined piecewise, and discontinuities can occur at the boundaries of the intervals, specifically at 0. Additionally, points where the greatest integer function changes value can lead to non-differentiability. In this case, there are two points of discontinuity and two points of non-differentiability, resulting in m+n=4.
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