If g(X) = 2+ln(x-5), find the inverse function, (g^(-1))(x)

Question

Solution:
y = 2+ ln(x-5)
e^y = 2 + x - 5
x = e^y + 3
y = e^x + 3
g^(-1) = y = e^x + 3

Is that right? I'm following an example - but don't really get it - how do I determine the domain and range - I know they flip when I do the inverse.

Answer 1

x = 2+ln(y-5)
x-2 = ln(y-5)
e^(x-2) = y-5

y = e^(x-2) + 5