Question

Exchange Rates The relative value of currencies fluctuates every day. When this problem was written, one Canadian dollar was worth 0.9766 U.S. dollars. (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?

Name: Problem 99, Chapter 2: Precalculus Mathematics for Calculus
Uploaded: 2020-06-24T17:50:34-08:00
Duration: 2 min 18 s
Channel: Vishal Parmar
Description: Exchange Rates The relative value of currencies fluctuates every day. When this problem was written, one Canadian dollar was worth 0.9766 U.S. dollars. (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?

   Exchange Rates The relative value of currencies fluctuates every day. When this problem was written, one Canadian dollar was worth 0.9766 U.S. dollars.
(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?

Precalculus Mathematics for Calculus

James Stewart,… 7th Edition

Chapter 2, Problem 99

Instant Answer

Solved by Expert Vishal Parmar

06/24/2020

Step 1

9766 U.S. dollars. We can express this as a function $f(x)$ that gives the U.S. dollar value of $x$ Canadian dollars. The function is $f(x)=0.9766x$. Show more…

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Exchange Rates The relative value of currencies fluctuates every day. When this problem was written, one Canadian dollar was worth 0.9766 U.S. dollars. (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?

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Key Concepts

Currency Conversion Calculation

This concept pertains to the application of the exchange rate function and its inverse to calculate how much money in one currency is equivalent to a specific amount in another currency. It involves substituting values into the function to determine the converted amounts.

Exchange Rate Function

This concept involves creating a mathematical function that converts an amount in one currency to its equivalent in another currency, using a fixed multiplier that represents the exchange rate. The function takes an input (the amount in the original currency) and outputs the corresponding value in the target currency.

Inverse Function

An inverse function reverses the process of the original function. It allows one to convert an amount from the target currency back to the original currency by applying the reciprocal of the exchange rate. This concept is essential for understanding bidirectional currency conversion.

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