Answer
Points lying inside the sphere of radius 2 are where $f(x, y)$ is continuous.
Work Step by Step
We are given that
\[
f(x, y, z)=\ln \left(4-x^{2}-y^{2}-z^{2}\right)
\]
So we have to find the domain of $f(x, y, z)$
We know that function $\ln P(x, y, y)$ has the domain $P(x, y, z)>0$. So here,
\[
\begin{array}{l}
4-x^{2}-y^{2}-z^{2}>0 \\
\Rightarrow x^{2}+y^{2}+z^{2}<4
\end{array}
\]
This denotes the points lying inside the sphere of radius 2 where $f(x, y)$ is continuous.
