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

问题描述:

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

f(-x)=-f(x) g(-x)=g(x)g(x+y) =e^(x+y)+e^-(x+y)=1/2*[(e^x+e^-x)(e^y+e^-y) + (e^x-e^-x)(e^y-e^-y)]=1/2*[g(x)g(y)+f(x)f(y)]g(x-y) 【-y 代替y】=1/2*[g(x)g(y)-f(x)f(y)][g(x+y)]/[g(x-y)]={1/2*[g(x)g(y)+...