Answer
\[
(x, y, z) \in\left\{\mathbb{R} -\text { except points on the cylinder } x^{2}+z^{2}=1\right\}
\]
Work Step by Step
We are given that
\[
f(x, y, z)=\frac{y+1}{x^{2}+z^{2}-1}
\]
We have to find the region where $f(x, y, z)$ is continuous
Region of continuity is the set of points in 3-d space except points on the cylinder whose axis is along the y-axis of radius $1,$ because the denominator is not defined on those points.
