Ok bit of help please guys - i think i'm just twisting myself in unnecessary knots!

The function:$\displaystyle g(x) = \frac{1}{9}(x - 3)^2 - 4 (6 \leq x \leq 9)$

Is the Domain[6,9]?

How can i then find the image set of$\displaystyle g^-1$and its rule?

Thank you