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.)

Question

Magdalena Garza

Mathematics

20 December, 02:45

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.)

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Answers (1)

Know the Answer?

Lilyana Guerra · 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

Step-by-step 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