Question

Let the functions $f :(-1,1) \rightarrow R$ and $g :(-1,1) \rightarrow(-1,1)$ be defined by
$f(x)=|2 x-1|+|2 x+1|$ and $g(x)=x-[x] \text {, }$
where $[ x ]$ denotes the greatest integer less than or equal to $x$. Let fog : $(-1,1) \rightarrow R$ be the composite function defined by $(f o g)(x)=f(g(x))$. Suppose $c$ is the number of points in the interval $(-1,1)$ at which fog is NOT continuous, and suppose $d$ is the number of points in the interval $(-1,1)$ at which fog is NOT differentiable. Then the value of $c + d$ is ____

Answer 1

Answer: $c + d = 4$