$y=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}+2$
$ \therefore\frac{y-2}{1}=\frac{e^{x}-e^{-x}}{e^{x}+e^{-x}}$
$\therefore\frac{y-2+1}{y-2-1}=\frac{e^{x}-e^{-x}+e^{x}+e^{-x}}{e^{x}-e^{-x}-e^{x}-e^{-x}}$ (યોગ-વિયોગ )
$\therefore\frac{y-1}{y-3}=\frac{2e^{x}}{-2e^{-x}}$
$\therefore e^{2x}=\frac{y-1}{3-y}$
$\therefore x=\frac{1}{2}log_{e}\left(\frac{y-1}{3-y}\right)$
$f^{-1}\left(x\right)=log_{e}\left(\frac{x-1}{3-x}\right)^{\frac{1}{2}}$
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