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
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![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