Find the Domain and Range of the Function $g ( x , y ) = x ^ { 2 } + 2 y ^ { 2 } + 3$

Multiple Choice

Find the domain and range of the function $g ( x , y ) = x ^ { 2 } + 2 y ^ { 2 } + 3$ .

A) $\begin{array} { l } D = \{ ( x , y ) \mid 0 \leq x < \infty , 2 \leq y < \infty \} \\R = \{ z \mid 0 \leq z \}\end{array}$
B) $\begin{array} { l } D = \{ ( x , y ) \mid - \infty < x < \infty , - \infty < y < \infty \} \\R = \{ z \mid 3 \leq z \}\end{array}$
C) $\begin{array} { l } D = \{ ( x , y ) \mid - \infty < x < \infty , 2 \leq y < \infty \} \\R = \{ z \mid - \infty < z < \infty \}\end{array}$
D) $\begin{array} { l } D = \{ ( x , y ) \mid 0 \leq x < \infty , 0 \leq y < \infty \} \\R = \{ z \mid 2 \leq z \}\end{array}$