JEE Math Practice Question

Let the functions $f:(-1,1) \rightarrow \mathbb{R}$ and $g:(-1,1) \rightarrow(-1,1)$ be defined by \[ f(x)=|2 x-1|+|2 x+1| \text { and } g(x)=x-[x] . \] where $[x]$ denotes the greatest integer less than or equal to $x$. Let $f \circ g:(-1,1) \rightarrow \mathbb{R}$ 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 what is the value of $c+d$?