一道函数题已知f(x)=e^x-e^-x,g(x)=e^x+e^-x(e=2.71……)设f(x)·f(y)=4g(x)·g(y)=8求g(x+y)/g(x-y)的值

Question

一道函数题
已知f(x)=e^x-e^-x,g(x)=e^x+e^-x(e=2.71……)
设f(x)·f(y)=4 g(x)·g(y)=8 求g(x+y)/g(x-y)的值

Answer 1

f(x)·f(y)=（e^x-e^(-x)）(e^y-e^(-y))=e^(x+y)+e^(-x-y)-e^(y-x)-e^(x-y)=4
g(x)·g(y)=（e^x+e^(-x)）(e^y+e^(-y))=e^(x+y)+e^(-x-y)+e^(y-x)+e^(x-y)=8
g(x+y)=[f(x)·f(y)+g(x)·g(y)]/2=6
g(x-y)=[g(x)·g(y)-f(x)·f(y)]/2=2
g(x+y)/g(x-y)=3