Fine D and R of the two functions.

a) f(x,y)=ln(√(1+x^{2}+y^{2})) the range can't be determined and the domain is R^{2}... why?

b) f(x,y,z)= 1/√(x^{2}+y^{2}+z^{2}-1) domain is R^{3}-B(0,1) = {(x,y,z)|abs(x,y,z)>1}..why is that the domain? I understand it haveing to be greater than one due to the fact that if it becomes 0 then its DNE

I don't understand how/why they are answering the problem in the way they do. I have the answer and it says a) definition of domain f=ln o √ o g is R^{2}. and for b) f= h o √ o g is R^{3}-B(0,1) = {(x,y,z)|abs(x,y,z)>1}.

is there any clarification needed, please ask. could use help on this.

Thanks!!!!!!