Hello from MrBillDoesMath!
Answer:
x >=4
Discussion:
The inverse of q is
-1 +\- (x-4)^(1/4) (the fourth root of x-4)
(Inverse found by solving x= (y+1)^4 +4 for y)
The domain of the inverse is therefore x such that x -4 >=0 , i.e. x >=4
Regards,
MrB
P.S. I'll be on vacation from Friday, Dec 22 to Jan 2, 2019. Have a Great New Year!