f(x)为奇函数,f(-x)=-f(x)
f(x)+f(-x)=0
即有
a+1/(2^x-1)+a+1/[2^(-x)-1]
=2a+1/(2^x-1)+1/[2^(-x)-1]
=2a+1/(2^x-1)+ 2^x/(1-2^x)
=2a+(1-2^x)/(2^x-1)
=2a-1
=0
所以a=1/2
f(x)=1/2+1/(2^x-1)
2^x>0
2^x-1>-1
1/(2^x-1)∈(-∞,-1)∪(0,+∞)
值域:(-∞,-1/2)∪(1/2,+∞)