A-Level Further Maths H4-04 Hyperbolic Inverse: Logarithmic Form of y=artanh(x)

[flooglewarp]

once you've gotten to the stage of making e^2y the subject, couldnt you express e^2y as (e^y)^2 then root both sides and expressing y as ln ( +- sqrt(x+1/1-x) ) ? or would that only work for |x| < 1 since log arg cant be negative