The inverse function of f(x)= 8^ 2 x -8^ -2 x 8^ 2 x +8^ -2 x , x (-1,1) , is

Mathematics · JEE Main · NTA Exams — Sets, Relations and Functions

1. \(\frac{1}{4} \log _{e}\left(\frac{1+x}{1-x}\right)\)
2. \(\frac{1}{4} \log _{e}\left(\frac{1-x}{1+x}\right)\)
3. \(\frac{1}{4}\left(\log _{1} e\right) \log _{2}\left(\frac{1+x}{1-x}\right)\)
4. \(\frac{1}{4}\left(\log _{1} e\right) \log _{2}\left(\frac{1-x}{1+x}\right)\)

Answer

(A) 1 4 _ e ( 1+x 1-x )

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