College Algebra, Chapter 3, 3.7, Section 3.7, Problem 80

Suppose that one Canadian dollar was worth $1. 0573$ U.S. dollar at a certain time.

a.) Find a function $f$ that gives the U.S. dollar value $f(x)$ of $x$ Canadian dollars.

b.) Find $f^{-1}$. What does $f^{-1}$ represent?

c.) How much Canadian money would $\$ 12,250$ in U.S. currency be worth?


a.) If 1 Canadian dollar = $1.0573$ U.S. dollar, then

$f(x) = 1.0573 x$

b.) To find $f^{-1}$, set $y = f(x)$


$
\begin{equation}
\begin{aligned}

y =& 1.0573 x
&& \text{Solve for $x$, divide } 1.0573
\\
\\
x =& \frac{y}{1.0573}
&& \text{Interchange $x$ and $y$}
\\
\\
y =& \frac{x}{1.0573}
&&

\end{aligned}
\end{equation}
$


Thus, $\displaystyle f^{-1} (x) = \frac{x}{1.0573}$.

If $f(x)$ represents the exchange rate of Canadian to U.S. dollar, then $f^{-1} (x)$ represents the exchange rate of U.S. dollar to Canadian dollar.

c.) If $x = \$12,250 $ U.S. dollar

then its equivalent Canadian dollar is..

$\displaystyle \frac{12,250}{1.0573} = 11,586.16$