If $f:A\rightarrow B$ is defined as $f(x)=\sqrt 3 sinx+cosx+4$ and $f$ is invertible then find A.

Question

(A) $\large[-\frac{2\pi}{3},\frac{\pi}{3}]$ (B) $\large[\frac{\pi}{6},\frac{5\pi}{6}]$ (C) $\large[-\frac{\pi}{2},\frac{\pi}{2}]$ (D) $\large[-\frac{\pi}{3},\frac{\pi}{3}]$