Question

若f(x)=1-[a/(e^x-1)]是奇函数,则a的值为

Answer 1

f(-x)=1-[a/(e^-x-1)]=1-[ae^x/(1-e^x)]=-f(x)=[a/(e^x-1)]-1,令t=e^x,显然t不能为1

1-[at/(1-t)]=a/(t-1)-1,

[2(t-1)+at]/(t-1)=a/(t-1),

(2+a)t-2=a,a=-2