Describe the domain and range of the function. $f ( x , y ) = \sqrt { 49 - x ^ { 2 } - y ^ { 2 } }$
A)domain: The disk $x ^ { 2 } + y ^ { 2 }

Question

Describe the domain and range of the function. $f ( x , y ) = \sqrt { 49 - x ^ { 2 } - y ^ { 2 } }$
A)domain: The disk $x ^ { 2 } + y ^ { 2 } < 49$ range: The interval (0,7)
B)domain: The disk $x ^ { 2 } + y ^ { 2 } < 49$ range: The interval [0,7]
C)domain: The disk $x ^ { 2 } + y ^ { 2 } \leq 49$ range: The interval [0,7)
D)domain: The disk $x ^ { 2 } + y ^ { 2 } \leq 49$ range: The interval [0,7]
E)domain: The disk $x ^ { 2 } + y ^ { 2 } < 49$ range: The interval [0,7)

Quizplus · Accepted Answer

The domain of $f(x, y) = \sqrt{49 - x^2 - y^2}$ includes all points $(x, y)$ for which the expression under the square root is non-negative, i.e., $49 - x^2 - y^2 \geq 0$, which simplifies to $x^2 + y^2 \leq 49$. This represents the disk including its boundary where the radius squared is 49. The range of the function is the set of all possible output values, which starts from 0 (when $x^2 + y^2 = 49$) up to 7 (when $x = 0$ and $y = 0$), inclusive, hence [0,7].

Describe the Domain and Range of the Function f(x,y)=49−x2−y2f ( x , y ) = \sqrt { 49 - x ^ { 2 } - y ^ { 2 } }f(x,y)=49−x2−y2​

Describe the Domain and Range of the Function $f ( x , y ) = \sqrt { 49 - x ^ { 2 } - y ^ { 2 } }$