Traders often buy foreign currency in hope of making money when the currency's value changes. For example, on June $5,2009,$ one U.S. dollar could purchase 0.7143 Euros, and one Euro could purchase 137.402 yen. Let $f(x)$ 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.
(b) Find a function that relates Euros to yen.
(c) Use the results of parts (a) and (b) to find a function that relates dollars to yen. That is, find $(g \circ f)(x)=$ $g(f(x))$
(d) What is $g(f(1000))$ ?