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Problems PreCal 1508 PLTL Workshop, September 9, 2011\\
PL: Alex Knaust, Lecturer: Yi-Yu Liao
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\begin{enumerate}
\item Determine if the pairs of functions are inverses of one another
\begin{enumerate}
	\item $f(x) = \frac{x^3}{2}, \quad g(x) = \sqrt[3]{2x}$
	\item $f(x) = \frac{x - 9}{4}, \quad h(y) = 4y + 9$
	\end{enumerate}
		\item The function given by $f(x) = k(2 - x - x^3)$ has an inverse function, and $f^{-1}(3) = - 2$. Find $k$. (\emph{Hint : Don't try to find the inverse function})
		
		\item Determine if the following functions have an inverse, and if they do find the inverse.
		\begin{enumerate}
		\item $h(x) = \frac{1}{x^4}$
		\item $g(x) = (x + 3)^2,\quad x \geq -3$
		\item $f(x) = \sqrt{2x + 3}$
		\end{enumerate}
		
		\item Restrict the domain of $f(x) = \frac{1}{2}x^2 - 1$ so that $f$ has an inverse function, then find the inverse function $f^{-1}$.
		
		\item Does $f$ have an inverse function?\\
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		\begin{tabular}{|c|c|}
\hline 
$x$ & $f(x)$ \\ 
\hline 
1 & 4 \\ 
\hline 
2 & 8 \\ 
\hline 
3 & 2 \\ 
\hline 
4 & 4 \\ 
\hline 
\end{tabular}
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\item If $f(x) = x + 1$ and $g(x) = 6x$, is $(f \circ g)(x) = (g \circ f)(x)$?

\item If $(f \circ g)(x) = \frac{(x+1)^2}{x+9}$ and $f(x) = \frac{x^2}{x + 8}$ what is $g(x)$?
\end{enumerate}
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