Let be defined by

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

Problem

Let f:(−1,1)→Bf:(-1,1)\rightarrow B be defined by f(x)=tan⁡−1(2x1−x2)f(x)=\tan^{-1}\left(\frac{2x}{1-x^2}\right). Then ff is both one-one and onto when BB is the interval (a) [−π2,π2]\left[-\frac{\pi}{2},\frac{\pi}{2}\right] (b) (−π2,π2)\left(-\frac{\pi}{2},\frac{\pi}{2}\right) (c) (0,π2)\left(0,\frac{\pi}{2}\right) (d) [0,π2)\left[0,\frac{\pi}{2}\right)

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