Question

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?

Solution

Verified
Step 1
1 of 2

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.

Create a free account to view solutions

Create a free account to view solutions

Recommended textbook solutions

Precalculus 2nd Edition by Carter, Cuevas, Day, Malloy

Precalculus

2nd EditionISBN: 9780076602186Carter, Cuevas, Day, Malloy
8,885 solutions
Nelson Functions 11 1st Edition by Chris Kirkpatrick, Marian Small

Nelson Functions 11

1st EditionISBN: 9780176332037Chris Kirkpatrick, Marian Small
1,275 solutions
Precalculus with Limits 3rd Edition by Larson

Precalculus with Limits

3rd EditionISBN: 9781133962885 (3 more)Larson
11,422 solutions
Precalculus: Mathematics for Calculus 7th Edition by Lothar Redlin, Stewart, Watson

Precalculus: Mathematics for Calculus

7th EditionISBN: 9781305071759 (4 more)Lothar Redlin, Stewart, Watson
9,756 solutions

More related questions

1/4

1/7