If f : R → S defined by $f(x)=\sin x-\sqrt{3}\cos x+1$ is onto, then what is the interval of S?

(–2, 2) [–2, 2] [–1, 3] $[-\sqrt{3},\sqrt{3}]$

[–1, 3]

$-\sqrt{1+(-\sqrt{3})^2}≤(\sin x-\sqrt{3}\cos x)≤\sqrt{1+(\sqrt{-3})^2}$ $-2≤(\sin x-\sqrt{3}\cos x)≤2$ $-2+1≤(\sin x-\sqrt{3}\cos x+1)≤2+1$ $-1≤(\sin x-\sqrt{3}\cos x+1)≤3$ i.e., Range = [-1, 3] For f to be onto S = [-1, 3]