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

Question

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

Quizplus · Accepted Answer

The domain of $g(x, y)$ is all real numbers for both $x$ and $y$ since there are no restrictions on these variables. The range is $z \geq 3$ because the minimum value of $x^2 + 2y^2$ is 0, making the minimum value of the function 3.

Find the Domain and Range of the Function g(x,y)=x2+2y2+3g ( x , y ) = x ^ { 2 } + 2 y ^ { 2 } + 3g(x,y)=x2+2y2+3

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