Yes the domain is [6,9].

The range can be found by finding f(6) and f(9).

and so the range is [-3,0]

When taking the inverse the the domain becomes the range and the range becomes the domain. Therefore the domain of is [-3,0] and the range is [6,9]

Let

.

To determine the sign find g^{-1}(0) = 9 = 3+3\sqrt{4} = 9. So we want the positive root:

Domain: [-3,0]

Range : [6,9]