The answer that you have is correct.

You would complete the square using +9

g(x)= (x-3)^{2 }+7-9 This is done to keep it balanced

g(x)= (x-3)^{2} +2

Switch the G(x) to y and reserve that x and y

x= (y-3)^{2}+2 Now solve for y

y= Squrt (x+2) +3

The domain is limited by the square rt. It can't be <0 So the domain is x< and = to -2.

You did a great job