Question

已知f(x)=1/2+(a+1)/[2(2^x-1)]为奇函数,求a

Answer 1

f(x)=1/2+(a+1)/[2(2^x-1)]

奇函数f(-x)=-f(x)

1/2+(a+1)/[2(2^(-x)-1)]=-1/2-(a+1)/[2(2^x-1)]

1+(a+1)2^x/[2(1-2^x)]=-(a+1)/[2(2^x-1)]=(a+1)/[2(1-2^x)]移项得

1=(a+1)/2

a=1