Think of a function as an equation from which X can be solved.
Get x = 2 y
Then change x into y, and change y into x to get the inverse function expression.
Y = 2 x
The domain of the inverse function is the domain of the original function.
y=log3 (x+6)
x+6=3^y
x=3^y -6
Inverse function y = 3 x-6
The range of the original function is r, so the domain of the inverse function is R.
So f- 1 (x) = 3 x-6 (x ∈ r)