问题详情:
已知f(x)=ex-e-x,g(x)=ex+e-x(e=2.718…).
(1)则[f(x)]2-[g(x)]2的值为 ;
(2)若f(x)·f(y)=4,g(x)·g(y)=8,则= .
【回答】
(1)-4 (2)3
(1)[f(x)]2-[g(x)]2
=[f(x)+g(x)][f(x)-g(x)]
=[(ex-e-x)+(ex+e-x)][(ex-e-x)-(ex+e-x)]
=2ex·(-2e-x)
=-4.
(2)因为f(x)·f(y)=(ex-e-x)(ey-e-y)
=ex+y-ex-y-ey-x+e-(x+y),
g(x)·g(y)=(ex+e-x)(ey+e-y)
=ex+y+ex-y+ey-x+e-(x+y),
g(x+y)=ex+y+e-(x+y),
g(x-y)=ex-y+e-(x-y)=ex-y+ey-x,
所以
解得
所以==3.
*:
知识点:基本初等函数I
题型:填空题