f(x)=(2^x-1)/(2^x+1)
=(2^x+1-2)/(2^x+1)
=1-2/(2^x+1)
2^x+1单增
2/(2^x+1)单减
-2/(2^x+1)单增
1-2/(2^x+1)单增
故函数f(x)在R上是增函数