Let f:−π$$3$$,$$2$$$$π$$$$3$$→[$$0$$,$$4$$] be a function defined as $$f(x)=3sin$$⁡x−$$cos$$⁡$$x+2$$ . Then f−$$1(x)$$ is given by

Correct option is 2sin−1⁡x−22+π6

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

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sin−1⁡x−22−π6

sin−1⁡x−22+π6

2π3+cos−1⁡x−22

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detailed solution

Correct option is B

y=f(x)=3sin⁡x−cos⁡x+2=2sin⁡x−π6+2------(1) Since f(x) is one-one and onto, f is invertible. From (1),sin⁡x−π6=y−22 or x=sin−1⁡y−22+π6 or f−1(x)=sin−1⁡x−22+π6

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Let f:−π3,2π3→[0,4] be a function defined as f(x)=3sin⁡x−cos⁡x+2 . Then f−1(x) is given by

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