求y=ln(x+√(x^2+1))的反函数

y=ln(x+√(x^2+1))
x+(x^2+1)^(1/2)=e^y
(x^2+1)^(1/2)=e^y-x
x^2+1=e^2y-2xe^y+x^2
2xe^y=e^2y-1
x=(e^y)/2-[e^(-y)]/2=[e^y-e^(-y)]/2
反函数：y=[e^x-e^(-x)]/2