How do you find & draw the domain of the function $\displaystyle f(x,y)=-\sqrt{x^2+y^2-121}-\frac{1}{\sqrt[7]{x-y}}$
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