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\noindent {\bf Problem statement} Suppose
$\displaystyle{Z(x)={{3x-5}\over{2x-1}}}$.

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\noindent a) Compute $Z'(x)$. What are $Z(1)$ and $Z'(1)$?

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\noindent b) Suppose $s$ is any number in the domain of $Z$, and
$t=Z(s)$. Solve this equation for $s$. Explain why solving this
equation verifies that $Z$ is one-to-one.

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\noindent c) Find $W$, the function inverse to $Z$, and compute $W'$.
What are $W(-2)$ and $W'(-2)$?

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\noindent d) Explain the relationships between the numerical answers
in a) and c).









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