Limits Continuity And Differentiability

For a real number $\alpha$, let $[\alpha]$ denote the greatest integer less than or equal to $\alpha$. For a finite set $S$, let $|S|$ denote the number of elements in the set $S$.

Consider the functions $f:(-3,3) \rightarrow(-\infty, \infty)$ and $g:(-3,3) \rightarrow(-\infty, \infty)$ defined by

\(f(x)=\left[x^3\right] \log _e\left(1+\sin ^2(\pi(x-[x]))\right)\)

and

\(g(x)=x^3 \sin ^2\left(\pi \log _e(1+x-[x])\right) .\)

Let

\(A=\{x \in(-3,3): f \text { is discontinuous at } x\}\)

and

\(B=\{x \in(-3,3): g \text { is discontinuous at } x\} .\)

Then the value of $|A|+2|B|-|A \cap B|$ is $\_\_\_\_$ .