g(x) = ln (x-2), x>2 (x is a real number)

 

The question says find g inverse. I have no problem finding the function, but I met difficulty in looking for the domain. The domain of g inverse is the range of g, but I cannot find the range of g, so do we have to state the domain of g inverse?

The range of a natural log is all real numbers, (as x-2 approaches 0, ln(x-2) approaches negative infinity, as x-2 approaches infinity, ln(x-2) approaches infinity) so you should be able to get your domain from that.

I cannot find the range of g(x)

You've already told us the range, and the domain of g(x)

[math']g(x) = \ln(x-2) \quad x>2 \quad x \in \mathbb{R}[/math]