What is the inverse of f (x)= ln(square root of x-1÷x+1)

Answer 1

y = ln √((x-1)/(x+1))
swap variables and solve for y again.
x = ln √((y-1)/(y+1))
e^x = √((y-1)/(y+1))
e^(2x) = (y-1)/(y+1)

e^(2x) + e^(2x) y = y - 1
y(e^(2x) - 1) = - (e^(2x)+1)

y = (1+e^(2x)) / (1-e^(2x))