I dont know if this is right...

i need inverse function of g(x)= -2(x+3)^2 +8 (-5less than or equal to x less than or equal to -3)

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

but this seems horribly wrong, - under a root and how do i find the domain from that??