$Iff:R\to S,definedbyf\left(x\right)=\sin x-\sqrt{3}\cos x+1,isonto,thenthe\mathrm{int}ervalofSis$

$\begin{array}{l}f\left(x\right)=\sin x-\sqrt{3}\cos x+1isonto\\ thenS=Rangeoff\left(x\right)\\ =[c-\sqrt{a^2+b^2},c+\sqrt{a^2+b^2}]\\ =[1-\sqrt{1+3},1+\sqrt{1+3}]\\ =[1-2,1+2]\\ =[-1,3]\end{array}$