字典网 问答 其它 已知函数f(x)=e^x-e^-x,g(x)=e^x+e^-x(1)求[f(x)]^2-[g(x)]^2的值(2)设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x-y)
问题标题:
已知函数f(x)=e^x-e^-x,g(x)=e^x+e^-x(1)求[f(x)]^2-[g(x)]^2的值(2)设f(x)f(y)=4,g(x)g(y)=8,求g(x+y)/g(x-y)
问题描述:

已知函数f(x)=e^x-e^-x,g(x)=e^x+e^-x

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

黄广连回答:
  f(x)+g(x)=2*e^x(f(x)+g(x))^2=4*e^2x   f(x)g(x)=e^2x-e^-2x{f(x)}^2+{g(x)}^2=2e^2x+2e^-2xf(x)f(y)=[e^x-e^-x][e^y-e^-y]   =e^(x+y)-e^(x-y)-e^[-(x-y)]+e^[-(x+y)]   =g(x+y)-g(x-y)=4   g(x)g(y)=[e^x+e^-x][e^y+e^-y]   =e^(x+y)+e^(x-y)+e^[-(x-y)]+e^[-(x+y)]   =g(x+y)+g(x-y)=8   解得:   g(x+y)=6   g(x-y)=2   因此:   g(x+y)/g(x-y)=3
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