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

question 124

Multiple Choice

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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