Chapter 14.1, Problem 27E

a)

To determine

The domain of the function $f\left(x,y\right)={\sin }^{-1}\left(y-x\right)$.

b)

To determine

The range of the function $f\left(x,y\right)={\sin }^{-1}\left(y-x\right)$.

c)

To determine

To explain: The level curves of the function $f\left(x,y\right)={\sin }^{-1}\left(y-x\right)$.

d)

To determine

The boundary of the domain of the function $f\left(x,y\right)={\sin }^{-1}\left(y-x\right)$.

e)

To determine

Whether the function $f\left(x,y\right)={\sin }^{-1}\left(y-x\right)$ is an open region, a closed region, or neither.

f)

To determine

To choose: Whether the domain of the function $f\left(x,y\right)={\sin }^{-1}\left(y-x\right)$ is bounded or unbounded.