\input epsf
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\magnification=\magstep1

\noindent {\bf Problem statement} It is true that $Q(x)= x^5+x^3+x$ is
a one-to-one function whose domain and range are all numbers.

\medskip

\noindent a) Graph $Q(x)$ on the interval $-2\le x\le 2$.

\medskip

\noindent b) Suppose that $R$ is the function inverse to $Q$. There is
no simple algebraic way to compute values of $R$. Compute $R(3)$,
$R'(3)$ and $R''(3)$.

\medskip

\noindent {\bf Hint} $Q(R(x))=x$ and $R(Q(x))=x$. So find an input to
$Q$ which will ``output'' 3. Then differentiate one of the equations,
maybe more than once.





\vfil\eject\end