The relative value of currencies fluctuates every day. When this problem was written, one Canadian dollar was worth 0.9766 U.S. dollars. Find f1.f^{-1}. What does f1f^{-1} represent?


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From part (a), f(x)=0.9766xf(x)=0.9766x. Finding the inverse gives:

y=0.9766xReplace f(x) with y.y0.9766=xDivide both sides by 0.9766.1.02396yxSimplify.1.02396x=ySwitch x and y.\begin{align*} y&=0.9766x&&\text{Replace $f(x)$ with $y$.}\\ \frac{y}{0.9766}&=x&&\text{Divide both sides by 0.9766.}\\ 1.02396y&\approx x&&\text{Simplify.}\\ 1.02396x&=y&&\text{Switch $x$ and $y$.} \end{align*}

The inverse is then f1(x)=1.02396xf^{-1}(x)=1.02396x. Since f(x)f(x) was the value in US dollars of xx Canadian dollars, then f1(x)f^{-1}(x) is the value in Canadian dollars of xx US dollars.

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