تابع $f(x) = \left\{ {\begin{array}{*{۲۰}{c}}
  {\frac{{۱ - \cos x}}{{۲b{x^۲}}}\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \gt ۰} \\ 
  {\left| {b - x} \right|\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x = ۰} \\ 
  {\left[ x \right] - ۲a\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,x \lt ۰} 
\end{array}} \right.$، یک تابع همواره پیوسته است. مقدار حقیقی $b-a$ کدام است؟