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\begin{flushleft} Recitation 2\hfill \course\\
2 September 1998 \hfill \semester \\
\medskip

Below is a selection of problems related to section 1.2.
These problems will not be collected or graded. However, you should
understand how to work each of these problems.  If you have questions,
please ask your TA or instructor. If you find a problem difficult,
consider working similar problems from the text for additional practice.

\begin{enumerate}
\item Work the following problems from Stewart: \S1.2, \#3, 5, 7, 13,
15, 23, 33, 35, 45, 47, 48, 51.  

\item Let $f(x) = x^2$, 
\begin{enumerate} \item Find a  formula for $f\circ f$.
\item Find a formula for $f\circ f\circ f$.
\item Find a formula for $f \circ f \circ f \circ f \circ f$.
\item Guess a formula for the $n$-fold composition 
$$
f\circ f\circ \dots \circ f.
$$
Here, the function $f$ appears $n$ times.

\end{enumerate}

\item If $ f(x) \ x^2 + 2x $ and $ g(x) = -1 + \sqrt x$.
\begin{enumerate}
\item What is the domain of $g$?
\item What is the range of $f$?
\item Find $f\circ g$.
\item Find $g\circ f$.  Be careful, the answer is not $x$!  For which $x$ is this function
defined?
\end{enumerate}

\item Are there any functions which are both even and odd?
\item A function is periodic with period $p$ if $f(x+p) = f(x)$. 
\begin{enumerate}
\item Give examples of functions which are periodic with period $2
\pi$. 
\item Give examples of functions which are periodic with period 1.
\item If $ f$ is periodic with period $p$, is $f(x+10)$ periodic? What
is the period.
\item If $f$ is periodic with period 1, is $f(2x)$ periodic? What is
the period?

\end{enumerate}
\end{enumerate}
\end{flushleft}
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