已知f(x)=e^x－e^﹣x,g(x)=e^x+e^﹣x(e=2.718…).设f(x)·f(y)=4,g(x)·g(

f(x)=e^x－e^﹣x,g(x)=e^x+e^﹣x
f(x)·f(y)=4,g(x)·g(y)=8.
∴[e^x-e^(-x)][e^y-e^(-y)]=4
==> [e^(x+y)+e^(-x-y)]-[e^(y-x)+e^(x-y]=4 ①
[e^x+e^(-x)][e^y+e^(-y)]=8
==> [e^(x+y)+e^(-x-y)]+[e^(x-y)+e^(y-x)]=8 ②
①+②:e^(x+y)+e^(-x-y)=6
②-①:e^(x-y)+e^(y-x)=2
g(x+y)/g(x-y)
=[e^(x+y)+e^(-x-y)]/[e^(x-y)+e^(y-x)]
=6/2
=3