Find the Domain and Range and Describe the Level Curves $$f ( x , y ) = \sin ^ { - 1 } \left( x ^ { 2 } + y ^ { 2 } \right)$$

Multiple Choice

Find the domain and range and describe the level curves for the function f(x,y) .
- $$f ( x , y ) = \sin ^ { - 1 } \left( x ^ { 2 } + y ^ { 2 } \right)$$

A) Domain: all points in the xy-plane; range: real numbers $- \frac { \pi } { 2 } \leq z \leq \frac { \pi } { 2 }$ ; level curves: circles with centers at $( 0,0 )$
B) Domain: all points in the $x y$ -plane satisfying $x ^ { 2 } + y ^ { 2 } \leq 1$ ; range: real numbers $- \frac { \pi } { 2 } \leq z \leq \frac { \pi } { 2 }$ ; level curves: circles with centers at $( 0,0 )$
C) Domain: all points in the $x y$ -plane satisfying $x ^ { 2 } + y ^ { 2 } \leq 1$ ; range: real numbers $- \frac { \pi } { 2 } \leq z \leq \frac { \pi } { 2 }$ ; level curves: circles with centers at $( 0,0 )$ and radii $r , 0 < r \leq 1$
D) Domain: all points in the $x y$ -plane; range: all real numbers; level curves: circles with centers at ( 0 , 0 )