Answer
a) For all $(x,y,z)$ such that $z \gt x^2+y^2+1$
b) For all $(x,y,z)$ such that $z \ne \sqrt {x^2+y^2}$
Work Step by Step
a) We can only take $\ln$ of positive values. Thus $z-x^2-y^2-1\gt 0$
b) There must not be zero in the denominator. So, for all $(x,y,z)$ such that $z \ne \sqrt {x^2+y^2}$
