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

Question

Dr. Abubacker · Accepted Answer

[Solution by Dr. Abubacker] $|x-2|$ is continuous, so discontinuities come from $[x]$ at $x=-1,0,1,2$: $m=4$. $f$ is not differentiable at those four points (and at $x=2$ the modulus kink coincides with one of them), so $n=4$. $m+n=8$. Answer (2).

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 :

Explanation

Reviewed by Dr. Abubacker

Want to attempt the full paper?