(b) $y = \frac{{{e^x} – {e^{ – x}}}}{{{e^x} + {e^{ – x}}}} + 2\,\, $

$\Rightarrow \,\,y = \frac{{{e^{2x}} – 1}}{{{e^{2x}} + 1}} + 2\,\,$

$ \Rightarrow \,\,{e^{2x}} = \frac{{1 – y}}{{y – 3}} = \frac{{y – 1}}{{3 – y}}\,\, $

$\Rightarrow \,\,x = \frac{1}{2}{\log _e}\,\left( {\frac{{y – 1}}{{3 – y}}} \right)$

$ \Rightarrow {f^{ – 1}}(y) = {\log _e}\,{\left( {\frac{{y – 1}}{{3 – y}}} \right)^{1/2}} $

$\Rightarrow {f^{ – 1}}(x) = {\log _e}{\left( {\frac{{x – 1}}{{3 – x}}} \right)^{1/2}}$.