Answer
All the points in 3 d space
Work Step by Step
We are given that
\[
f(x, y, z)=\sin \sqrt{x^{2}+y^{2}+3 z^{2}}
\]We have to find the domain of $f(x, y, z)$
$\sin x$ is defined for all the real numbers and $\sqrt{h(x, y, z)}$ is defined for all the points which satisfy $h(x, y, z) \geq 0$. So here,
\[
x^{2}+y^{2}+3 z^{2} \geq 0
\]
So, the equation is satisfied for all the real numbers in 3 d space, so it is continuous for all the points in 3 d space.
