Chapter 14: Partial Derivatives - Section 14.2 - Limits and Continuity in Higher Dimensions - Exercises 14.2 - Page 796: 34

a) For all (x,y) except the lines $x=2$and $x=1$ b) For all (x,y) except parabola $y=x^2$

a) There must not be zero on the denominator. After factoring the denominator we have $(x-2)(x-1)$, so we can see that the given function is defined for all $(x,y)$ except the lines $x=2$and $x=1$ b) When $x^2-y\neq 0$ and $y \ne x^2$, then there can be no zero in the denominator.