\def\wsn{31}
\input worksheet.tex

\item{1.}  Determine the domain and range of each of the following
functions:
$$
\pt a f(x)=\sin^{-1}x\hskip1in
\pt b g(x)=\sin^{-1}x^2\hskip1in
\pt c h(x)=\sin^{-1}(x^2-1)
$$

\bigskip
\item{2.} Determine whether each of the following equations is true or
false.  If true, give the reason it is true.  If false, give a
counterexample to the statement.

\medskip
\itemitem{a)} $\sin^{-1}(\sin x)=x$ for all $x$.

\medskip
\itemitem{b)} $\sin(\sin^{-1}x)=x$ for all $x$.

\medskip
\itemitem{c)} $\sin^{-2}x=\displaystyle{1\over(\sin x)^2}$ for $x\neq
n\pi$ where $n$ is an integer.  

\medskip
\itemitem{d)} $\sin^{-1}x=\displaystyle{1\over\sin x}$  for $x\neq
n\pi$ where $n$ is an integer.  

\medskip
\itemitem{e)} $\tan(\sin^{-1}x)=\displaystyle{1\over\sqrt{x^2-1}}$
when $-1