已知函数f(x)=㏒[(kx-1)/(x-1)](k∈R且k＞0)

f(x)=lg[(kx-1)/(x-1)](k∈R且k＞0)
(kx-1)/(x-1)>0,
讨论:
1)当0<K<1时,(kx-1)/(x-1)>0,有
X>1/K或X<1,
2)当K>1时,,(kx-1)/(x-1)>0,有
X>1或X<1/K.
即,函数的定义域为:{X|X>1/K或X<1,(0<K<1)}
或{X|X>1或X<1/K.(K>1)}

函数f(x)在[10，+∞)上单调递增,
f(x)=lg[(kx-1)/(x-1)](k∈R且k＞0)
f(x)=lg[(10k-1)/(10-1)],
(10k-1)/(10-1)>0,
k>1/10,
令,Y=(KX-1)/(X-1),求导,
Y'=[(KX-1)'(X-1)-(X-1)'(KX-1)]/(X-1)^2
=(1-K)/(X-1)^2,
当Y'=0时,有K=1,
因为K>0,而K>1/10,则有
当1/10<K<1时,Y'>0,则f(x)是增函数,
当K>1时,Y'<0,则f(x)J是减函数.
因为:函数f(x)在[10，+∞)上单调递增,即,
1/10<K<1.为k的取值范围