Question

Please help me find the domain of f(x,y,z)=z-x^2-y^2

Answer 1

@TuringTest please! Im doing a past paper

Answer 2

The domain of this is all reals, because \[f(x,y,z)\text{ is defined for all }x,y,z\in\mathbb R\] if it were f(x,y,z)=d on the other hand, that would be different

Answer 3

for instance if it were\[f(x,y,z)=z-x^2-y^2=0\]that would be a parabaloid\[z=x^2+y^2\]and since this says that since z>0, the domain of f would be\[x,y,z\in\mathbb R|z\ge0\]

Answer 4

Thank you I now understand. How can I think like you?