Is this function $f$ defined at the origin?

Question

$$f(x,y,z)=\ln{\sqrt{x^2+y^2+z^2}}$$

Is the function defined at the origin?

If so, what is its value and if not, give the reason.

Answer 1

One may recall that $$ \ln :(0,\infty)\mapsto \mathbb{R} $$ and $$ \sqrt{ 0^2+0^2+0^2}=0 $$ the given function is not defined at $(x,y,z)=(0,0,0)$.