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Class 12 Maths · Relations And Functions · Mcq Single Correct #95

Let \(f:(-1,1)\to B\), \(f(x)=\tan^{-1}\left(\frac{2x}{1-x^2}\right)\), be one-one and onto. Then \(B\) equals

✅ Step-by-Step Solution

Final Answer: Option (C): \((-\pi/2,\pi/2)\)
  1. For \(-1<x<1\), \(2\arctan x\in(-\pi/2,\pi/2)\). Thus principal arctangent gives \(f(x)=2\arctan x\), strictly increasing onto \((-\pi/2,\pi/2)\).

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