Let be defined by

MATHEMATICS · Single correct · A Level · Mathematics · Algebra and Functions · Algebra and Functions

Problem

Let f:[π3,2π3]→[3,4]f:\left[\frac{\pi}{3},\frac{2\pi}{3}\right]\to[3,4] be defined by f(x)=3sin⁡x−cos⁡x+2f(x)=\sqrt{3}\sin x-\cos x+2. Then f−1(x)f^{-1}(x) is given by (a) sin⁡−1(x−22)−π6\sin^{-1}\left(\frac{x-2}{2}\right)-\frac{\pi}{6} (b) sin⁡−1(x−22)+π6\sin^{-1}\left(\frac{x-2}{2}\right)+\frac{\pi}{6} (c) 2π3+cos⁡−1(x−22)\frac{2\pi}{3}+\cos^{-1}\left(\frac{x-2}{2}\right) (d) None of these

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