You have done exactly right- that is the formula for and you don't need to do anything else. If you really want to you might 'simplify' that a little as .
Yes, the domain and range swap for the inverse function. Here, the domain of f is x> 2 (actually, that's the "natural domain". If [tex]x\le 2[tex] then and ln(x) is only defined for x> 0) and the range is all real number (x very close to 2 will give 3x- 6 very close to 0 and so ln(3x- 6) "very close to " while if x is arbitrarily large, ln(3x- 6) is "very close to ". So the domain of is all real numbers and its range is y> 2.