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The inverse function of \(f\left(x\right)=\frac{{8}^{2x}-{8}^{-2x}}{{8}^{2x}+{8}^{-2x}},x\in \left(-1,1\right)\), is [JE…

Q1

The inverse function of \(f\left(x\right)=\frac{{8}^{2x}-{8}^{-2x}}{{8}^{2x}+{8}^{-2x}},x\in \left(-1,1\right)\), is

[JEE Main 2020, 8 Jan (Shift 1)]

a

\(\frac{1}{4}\left({\log }_{8}e\right){\log }_{e}\left(\frac{1-x}{1+x}\right)\)

b

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

c

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

d

\(\frac{1}{4}\left({\log }_{8}e\right){\log }_{e}\left(\frac{1+x}{1-x}\right)\)

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