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.

There are many possible descriptions, such as the set of all $(x,y)$ such that $x+y\lt 7$. That to me is the nicest, because it is quite symmetrical. 
But it can be rewritten, as you did, as the set of all $(x,y)$ such that $y\lt 7-x$. You don't want $y\le 7-x$, since $\ln$ is not defined at $0$. 
