Define a composite function, g ( f ( n ) ) , that determines the number of Japanese yen Bella will receive when having n U.S. dollars converted to Japanese yen.
To define a composite function ( g(f(n)) ) that determines the number of Japanese yen Bella will receive when converting ( n ) U.S. dollars, we need to establish two functions:
Function ( f(n) ): This function will convert U.S. dollars to Japanese yen based on the current exchange rate. Let's denote the exchange rate as ( r ) yen per U.S. dollar. Therefore, the function ( f(n) ) can be defined as:
[ f(n) = n \times r ]
where ( n ) is the amount in U.S. dollars and ( r ) is the exchange rate (yen per dollar).
Function ( g(x) ): This function will represent the final amount of yen received after any additional processing or fees, if applicable. For simplicity, let's assume there are no additional fees, so ( g(x) ) can simply return the value of ( x ):
[ g(x) = x ]
Now, we can define the composite function ( g(f(n)) ):
[ g(f(n)) = g(n \times r) = n \times r ]
Thus, the composite function ( g(f(n)) ) gives the total amount of Japanese yen Bella will receive when converting ( n ) U.S. dollars at the exchange rate ( r ).
In summary, the composite function is:
[ g(f(n)) = n \times r ]
where ( r ) is the exchange rate in yen per U.S. dollar.