$$\eqalign{
& f\left( x \right) = \sin x - \cos x + x\sqrt 3 \,\,\left( {D = R} \right) \cr
& f'\left( x \right) = \cos x + \sin x + \sqrt 3 \cr
& Do\,\,\sin x + \cos x \in \left[ { - \sqrt 2 ;\sqrt 2 } \right] \cr
& \Rightarrow f'\left( x \right) > 0\,\,\forall x \cr
& \Rightarrow Ham\,\,so\,\,DB/R \cr} $$