Find the Domain and Range of the Function $f ( x , y , z ) = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } - z ^ { 2 } }$

Find the domain and range of the function $f ( x , y , z ) = \sqrt { 4 - x ^ { 2 } - y ^ { 2 } - z ^ { 2 } }$ .

A) $\begin{array} { l } D = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 4 \right\} \\R = \{ w \mid 0 \leq w \leq 2 \}\end{array}$
B) $\begin{array} { l } D = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \leq 4 \right\} \\R = \{ w \mid 0 \leq w \}\end{array}$
C) $\begin{array} { l } D = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \geq 4 \right\} \\R = \{ w \mid 0 \leq w \}\end{array}$
D) $\begin{array} { l } D = \left\{ ( x , y , z ) \mid x ^ { 2 } + y ^ { 2 } + z ^ { 2 } \geq 4 \right\} \\R = \{ w \mid 0 \leq w \leq 2 \}\end{array}$

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