f(x)=e^x-e^-x,g(x)=e^x+e^-x,1、求[f(x)]^2-[g(x)]^2的值设f(x)f(y)=4,g(x)g(y)=8,求[g（x+y）]/[g（x-y）]的值

f(x)=e^x-e^-x,g(x)=e^x+e^-x,1、求[f(x)]^2-[g(x)]^2的值设f(x)f(y)=4,g(x)g(y)=8,求[g（x+y）]/[g（x-y）]的值
f(x)=e^x-e^-x,g(x)=e^x+e^-x,1、求[f(x)]^2-[g(x)]^2的值
设f(x)f(y)=4,g(x)g(y)=8,求[g（x+y）]/[g（x-y）]的值

f(x)=e^x-e^-x,g(x)=e^x+e^-x,1、求[f(x)]^2-[g(x)]^2的值设f(x)f(y)=4,g(x)g(y)=8,求[g（x+y）]/[g（x-y）]的值
[f(x)]^2-[g(x)]^2==[f(x)+g(x)][f(x)-g(x)]=(2e^x)X(-2e^-x)=-4
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
所以e^（x+y)+e^-（x+y)=12/2=6
e^（x-y)+e^（y-x)=2
g（x+y)=e^（x+y)=+e^-（x+y)=6
g（x-y）=e^（x-y)+e^（y-x)=2
所以[g（x+y）]/[g（x-y）]=3

[f(x)]^2-[g(x)]^2=[f(x)+g(x)][f(x)-g(x)]=(2e^x)X(-2e^-x)=-4