First you have to prove that g is bijective, if you do that the problem is like solved.

"so i got... x= -2(y+3)^2 +8

x-8=-2(y+3)^2

-1/2(x-8)= (y+3)^2

square root both sides gives g-1(x)= √ -1/2(x-8)-3"

I don't understand - you should just calculate, then find (or do that when you prove that g is surjective) and the root that is in the interval you want it to be.