## Thomas' Calculus 13th Edition

$\{(x,y)\in \mathbb{R}^{2}\ \ |\ \$ $x\neq 1$ , $y\neq-1$ $\}$
$f$ is defined when the argument of the logarithm function is positive, $xy+x-y-1 \gt 0$ $x(y+1)-(y+1) \gt 0$ $(x-1)(y+1) \gt 0$ So, the domain of f is the whole plane $\mathbb{R}^{2}$, except the two lines $\left\{\begin{array}{l} x=1\\ y=-1 \end{array}\right.$ (Being excluded, the lines are graphed with dashed lines.) Domain: $\{(x,y)\in \mathbb{R}^{2}\ \ |\ \$ $x\neq 1$ , $y\neq-1$ $\}$