so to find the inverse you just switch the x and y and solve for y.
So if you have g(x) = y = ln sqrt (x+2)
you change it to x = ln sqrt (y+2) and solve for y:
x^e = sqrt(y+2)
x^2e = y+2
and if you want g inverse of 0, then you just plug in 0=x.
edit: woops, a minute too late. haha.