Let \[f:\left[ -\frac{\pi }{3},\frac{2\pi }{3} \right]\to [0,4]\] be a function defined as \[f(x)=\sqrt{3}\sin x-\cos x+2\].Then \[{{f}^{-1}}(x)\]is given by

\[\frac{2\pi }{3}+{{\cos }^{-1}}\left( \frac{x-2}{2} \right)\]

\[{{\sin }^{-1}}\left( \frac{x-2}{2} \right)-\frac{\pi }{6}\]

\[{{\sin }^{-1}}\left( \frac{x-2}{2} \right)+\frac{\pi }{6}\]

Let \[f:\left[ -\frac{\pi }{3},\frac{2\pi }{3} \right]\to [0,4]\] be a

1.	Let \[f:\left[ -\frac{\pi }{3},\frac{2\pi }{3} \right]\to [0,4]\] be a function defined as \[f(x)=\sqrt{3}\sin x-\cos x+2\].Then \[{{f}^{-1}}(x)\]is given by
A.	\[{{\sin }^{-1}}\left( \frac{x-2}{2} \right)-\frac{\pi }{6}\]
B.	\[{{\sin }^{-1}}\left( \frac{x-2}{2} \right)+\frac{\pi }{6}\]
C.	\[\frac{2\pi }{3}+{{\cos }^{-1}}\left( \frac{x-2}{2} \right)\]
D.	none of these
Answer» C. \[\frac{2\pi }{3}+{{\cos }^{-1}}\left( \frac{x-2}{2} \right)\]

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Let \[f:\left[ -\frac{\pi }{3},\frac{2\pi }{3} \right]\to [0,4]\] be a function defined as \[f(x)=\sqrt{3}\sin x-\cos x+2\].Then \[{{f}^{-1}}(x)\]is given by

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