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{\bf Math 165: Honors Calculus I}
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{\bf Quiz 8}\quad {\sl Nov.\ 5, 1998}

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\item
  \begin{enumerate}[a)]

  \item State \textsc{Bolzano's Theorem}.
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  \item State the \textsc{Intermediate Value Theorem}.
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  \end{enumerate}

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\item Prove that the equation $\cos(x) = x$ has a solution.
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\item Let $f(x) = \frac{x}{x+1}$ for $x > -1$.
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  \item Show that $f(x)$ is one-to-one in its domain $x > -1$.
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  \answerspace

  \item Find a formula for $f^{-1}(x)$ and determine its domain.
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