for the term 1/(x-y)^(1/7) we have all 2 space except y = x this line must be eliminated from the domain

for the term sqrt(x^2 +y^2 -121)

We must have

x^2 +y^2 -121>0

x^2 + y^2>121

this is everything on the boundary and outside the circle of radius 11

See attachment --domain in red