describe the domain of a function $f(x, y)$ Describe the domain of the function $f(x,y) = \ln(7 - x - y)$. I have the answer narrowed down but I am not sure if it would be $\{(x,y) \mid y ≤ -x + 7\}$ or $\{(x,y) \mid y < -x + 7\}$ please help me.

The domain is the locus of points $D=\{(x,y)\in\mathbb R^2 | 7-x-y>0\}$. You just need to work on the inequality, now. Of course you should know the domain of $\log$...
