题目
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= .
答案:(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. 答案: