JEE Advanced · 2020 · 27 Sep 2020 · Paper 2 · Continuity and Differentiability

Let the functions $f:(-1,1)\to \mathbb{R}$ and $g:(-1,1)\to (-1,1)$ be defined by

where $[x]$ denotes the greatest integer less than or equal to $x$. Let $f\circ g:(-1,1)\to \mathbb{R}$ be the composite function defined by $(f\circ g)(x)=f(g(x))$. Suppose $c$ is the number of points in the interval $(-1,1)$ at which $f\circ g$ is NOT continuous, and suppose $d$ is the number of points in the interval $(-1,1)$ at which $f\circ g$ is NOT differentiable. Then the value of $c+d$ is ____