$f(x) = \sqrt {\left| {{{\sin }^{ - 1}}\left| {\sin x} \right|} \right| - {{\cos }^{ - 1}}\left| {\cos x} \right|} $ is
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$f\left( x \right) = \left[ x \right] + \left| {1 - x} \right|,\, - 1 \le x \le 3$ where $[x]$ is the greatest integer function
Statement $1$ :$f$ is not continuous at $x = 0, 1, 2$ and $3$
Statement $2$ :$f\left( x \right) = \left( \begin{array}{l}
- x,\,\,\,\,\,\,\,\,\, - 1 \le x < 0\\
1 - x,\,\,\,\,\,\,\,0 \le x < 1\\
1 + x,\,\,\,\,\,\,\,1 \le x < 2\,\\
2 + x,\,\,\,\,\,\,2 \le x \le 3
\end{array} \right.$