Question

Traders often buy foreign currency in hope of making money when the currency's value changes. For example, on a particular day, one U.S. dollar could purchase 0.8869 Euros, and one Euro could purchase 143.1126 yen. Let fix) represent the number of Euros you can buy with x dollars, and let g(x) represent the number of yen you can buy with x Euros. (a) Find a function that relates dollars to Euros fx)Simplify your answer.) (b) Find a function that relates Euros to yen. gxSimplify your answer.) (c) Use the results of parts (a) and (b) to find a function that relates dollars to yen. That is, find (g o f)(x)-g(fx g(f(x)) Simplify your answer. Use integers or decimals for any numbers in the expression. Round to four decimal places as needed.) (d) What is g(1000))? g(f(1000)) Type an integer or decimal rounded to one decimal place as needed.)

Answer 1

(a)f(x)=0.8869x

(b)g(x)=143.1126x

(c)g(f(x))=126.9266x

(d)g(f(1000))=126926.6 Yen

Explanation:

Given on a particular day

• One U.S. dollar could purchase 0.8869 Euros
• One Euro could purchase 143.1126 yen

(a)If x represents the number of Dollars

Since one can purchase 0.8869 Euro with 1 USD, the function f(x) is a direct relationship where x is dollars and f(x) is in Euros.

• f(x)=0.8869x

(b)If x represents the number of Euros

Since one can purchase 143.1126 yen with 1 Euros, the function g(x) is a direct relationship where x is Euros and g(x) is in Yen.

• g(x)=143.1126x

(c)Given:

• g(x)=143.1126x

• f(x)=0.8869x

g(f(x))=143.1126(0.8869x)

• g(f(x))=126.9266x

(d)g(f(1000))

• g(f(x))=126.9266x

• g(f(1000))=126.9266 X 1000 =126926.6 Yen