Let the functions $f: (-1,1) \rightarrow \mathbb{R}$ and $g: (-1,1) \rightarrow (-1,1)$ be defined by $$f(x) = |2x - 1| + |2x + 1| \quad \text{and} \quad g(x) = x - [x],$$ 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 the value of $c + d$ is $\_\_\_\_$
Let the functions $f: (-1,1) \rightarrow \mathbb{R}$ and $g: (-1,1) \rightarrow (-1,1)$ be defined by
$$f(x) = |2x - 1| + |2x + 1| \quad \text{and} \quad g(x) = x - [x],$$
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 the value of $c + d$ is $\_\_\_\_$