Answer
${(x,y)∈R^{2}|y\gt -x-1}$
Work Step by Step
Given: $f(x,y)=ln(x+y+1)$
Since we can only take the logarithmic of positive quantities, we want $x+y+1\gt0$
This implies
$y\gt -x-1$
Therefore, the domain for given function is
${(x,y)∈R^{2}|y\gt -x-1}$
Sketch the graph for the domain as shown below:
