# Math Help - Domain of a multivariable function

1. ## Domain of a multivariable function

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

2. 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

3. Appreciate the help!