Chapter 14 - Partial Derivatives - 14.2 Limits and Continuity - 14.2 Exercises - Page 951: 34

$D=$ {$(x,y) | x-y \gt -1$}

As we are given that $G(x,y)=ln(1+x-y)$ The function $G(x,y)=ln(1+x-y)$ represents a logarithmic function which cannot be less than $0$ and exists only for positive numbers. Thus, $ 1+x-y \gt 0$ or, $x-y \gt -1$ or, $x-y \gt -1$ This means that $x \gt y-1$ Hence, Domain: $D=$ {$(x,y) | x-y \gt -1$}