f(-x)=1/[2^(-x)-1]+1/[2^(-x)+1]
=2^x/(1-2^x)+2^x/(1+2^x)
=-2^x/(2^x-1]+2^x/(2^x+1)
=(-2^x+1-1)/(2^x-1)+(2^x+1-1)/(2^x+1)
=-1-1/(2^x-1)+1-1/(2^x+1)
=-1/(2^x-1)-1/(2^x+1)
=-[1/(2^x-1)+1/(2^x+1)]
=-f(x)
所以函数是奇函数
f(-x)=1/[2^(-x)-1]+1/[2^(-x)+1]
=2^x/(1-2^x)+2^x/(1+2^x)
=-2^x/(2^x-1]+2^x/(2^x+1)
=(-2^x+1-1)/(2^x-1)+(2^x+1-1)/(2^x+1)
=-1-1/(2^x-1)+1-1/(2^x+1)
=-1/(2^x-1)-1/(2^x+1)
=-[1/(2^x-1)+1/(2^x+1)]
=-f(x)
所以函数是奇函数