f（x）=log1/2(x+1)/(x-1) ,函数在x>1的情况下是增函数,若x>=3,f(x)>(1/2)x+m,恒成立,求实数m的取值范围

f（x）=log1/2(x+1)/(x-1) ,函数在x>1的情况下是增函数,若x>=3,f(x)>(1/2)x+m,恒成立,求实数m的取值范围
f（x）=log1/2(x+1)/(x-1) ,函数在x>1的情况下是增函数,
若x>=3,f(x)>(1/2)x+m,恒成立,求实数m的取值范围

f（x）=log1/2(x+1)/(x-1) ,函数在x>1的情况下是增函数,若x>=3,f(x)>(1/2)x+m,恒成立,求实数m的取值范围
f（x）=log1/2(x+1)/(x-1)
x≠±1
f（x）=log1/2(x+1)/(x-1)
=log2(x-1)/(x+1)
=log2(1-2/(x+1))
x1,x+1是增函数,2/(x+1)是减函数,
所以-2/(x+1)是增函数,
即1-2/(x+1)也是增函数
所以log2(1-2/(x+1))也是增函数
f（x）=log1/2(x+1)/(x-1) ,函数在x>1的情况下是增函数,