Answer
The domain $D$ consists of all points $\left( {y,z} \right)$ not lying on the parabola $z = - {y^2}$.
$D = \left\{ {\left( {y,z} \right)|z \ne - {y^2}} \right\}$
Work Step by Step
The function $g\left( {y,z} \right) = \frac{1}{{z + {y^2}}}$ is defined only when $z + {y^2} \ne 0$ or $z \ne - {y^2}$. Thus, the domain $D$ consists of all points $\left( {y,z} \right)$ not lying on the parabola $z = - {y^2}$.
$D = \left\{ {\left( {y,z} \right)|z \ne - {y^2}} \right\}$
