\input epsf
\nopagenumbers
\magnification=\magstep1

\noindent {\bf Problem statement} Suppose that $f$ is the function
defined by the formula

$$f(x)={\biggl( \arctan \Bigl( \ln \bigl( \sqrt{x} -1 \bigr) \Bigr)
\biggr)^{\! 3} }\, .$$

\noindent a) What are the domain and range of $f$?  Answers should
{\it not} be numerical approximations, but should be written if needed
in terms of traditional constants such as $\pi$ and $e$.

\medskip

\noindent b) If $y=f(x)$, write a formula for $x$ in terms of $y$.

\vfil\eject\end