[Mastermander]

จาก $ 2x = e^y - e^{-y} $
$$ 2xe^y = e^{2y} - 1 $$
ให้ $ e^y = Z $ จะได้ว่า
\[ Z^2-2xZ-1 = 0 \]
\[ Z = \frac{2x\pm\sqrt{4x^2+4}}{2} \]
$$ Z = x + \sqrt{x^2+1} $$
$$ e^y = x + \sqrt{x^2+1} $$
$$ \ln e^y =\ln (x + \sqrt{x^2+1}) $$
$$ y = \ln (x + \sqrt{x^2+1}) $$
$$ f^{-1}(x) = \ln (x + \sqrt{x^2+1}) $$