Let f:(-2,2) R be defined by f(x)= array|c|c| x[x], & -2

Question

Let $f:(-2,2)	o R$ be defined by $f(x)= \begin{array}{|c|c|} x[x], & -2<x<0 \ (x-1)[x], & 0\le x\le 2 \end{array}$ where $[x]$ denotes the greatest integer function. If m and n respectively are the number of points in $(-2,2)$ at which $y=|f(x)|$ is not continuous and not differentiable, then $m+n$ is equal to \_\_\_\_\_\_\_\_\_\_\_\_.

Answer: 4

Accepted Answer

Given function is $f(x)= $$x[x], \& -2$$

Clearly, $|f(x)|$ remains same.

Given that, $m$ and $n$ respectively are the number points in $(-2,2)$ at which $y=|f(x)|$ is not continuous and not differentiable

So, $m=1$ where $y=|f(x)|$ not continuous

and $n=3$ where $|f(x)|$ is not differentiable.

Thus, $

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