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

question 315

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 )

---

Definitions:

Overvalued

A financial situation where the price of an asset exceeds its intrinsic value.

Board of Directors

A group of individuals elected by the shareholders of a corporation to oversee the management and make major decisions affecting the company's policy and strategy.

MBCA

The Model Business Corporation Act, a set of statutory provisions designed for the incorporation and operation of a business corporation.

Incorporator

The individual or entity that files the articles of incorporation, thus legally forming a corporation.