作业帮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
来源：学生作业帮助网 编辑：作业帮 时间：2024/04/29 06:31:31
![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](/uploads/image/z/11523359-47-9.jpg?t=f%28x%29%3De%5Ex-e%5E-x%2Cg%28x%29%3De%5Ex%2Be%5E-x%2C1%E3%80%81%E6%B1%82%5Bf%28x%29%5D%5E2-%5Bg%28x%29%5D%5E2%E7%9A%84%E5%80%BC%E8%AE%BEf%28x%29f%28y%29%3D4%2Cg%28x%29g%28y%29%3D8%2C%E6%B1%82%5Bg%EF%BC%88x%2By%EF%BC%89%5D%2F%5Bg%EF%BC%88x-y%EF%BC%89%5D%E7%9A%84%E5%80%BC)
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