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\begin{center}
{\LARGE Week 3, Due Fri 10/18}
\end{center}


\begin{enumerate}


\item Spivak, Chapter 3, Problems: $6,8,13$.
\item Spivak, Chapter 4,  Problem $5$ (pictures alone suffice; let \(a=b=1\) in part (ii)).

\item Say that a function \(f(x)\) with domain \(\Omega \) and that takes
values in \(\Omega\) can be ``halved'' if there exists
a function \(g(x)\) such that \(g(g(x)) = f(x)\).
\begin{enumerate}
\item Show that the function \(f(x) = x^r\) on the domain \(\Omega = (0,\infty)\)
can be halved if \(r > 0\).
\item(*) Find some function \(f(x)\) on \((0,\infty)\) with positive values
that cannot be halved. Warning: there is no requirement or assumption
that \(f(x)\) is continuous, whatever that means.
\end{enumerate}


\item(*) Spivak, Chapter 4, Problem $20$.

\end{enumerate}






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