1) 1+x/1-x>0,则-1x2>-1
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)(1-x2)]/[(1+x2)/(1-x1)]
[(1+x1)(1-x2)]/[(1+x2)/(1-x1)]>1
log2[(1+x1)(1-x2)]/[(1+x2)/(1-x1)]>0
f(x1)>f(x2)
f(x)在区间(-1,1)上为增函数
1) 1+x/1-x>0,则-1x2>-1
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)(1-x2)]/[(1+x2)/(1-x1)]
[(1+x1)(1-x2)]/[(1+x2)/(1-x1)]>1
log2[(1+x1)(1-x2)]/[(1+x2)/(1-x1)]>0
f(x1)>f(x2)
f(x)在区间(-1,1)上为增函数