Question

求y=ln(x+√(x^2+1))的反函数

Answer 1

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