(1)f(-x)=log2[(1-x)/(1+x)]=log2{[(1+x)/(1-x)]^(-1)}=-log2[(1+x)/(1-x)]=-f(x) 故为奇函数
(2)f'(x)=2ln2(1+x)/[(1-x)^3],令启前晌f'(x)>0,得-1
(3)f(x1)+f(x2)
=log2[(1+x1)/(1-x1)]+log2[(1+x2)/(1-x2)]
=log2[(1+x1)/(1-x1)*(1+x2)/(1-x2)]
=log2[(1+x1+x2+x1x2)/(1+x1x2-x1-x2)] (注:此处分子分母都除以 1+x1x2)
=log2[1+(x1+x2)/(1+x1x2)]/悔慎[1-(x1+x2)/(1+x1x2)]
=f((x1+x2)/(1+x1x2))