分式有意义,cosx -1≠0cosx≠1
x≠2kπ(k∈Z)
函数的定义域为(2kπ,2k+2π)(k∈Z)

y=(cosx -2)/(cosx -1)
ycosx -y=cosx -2
(y-1)cosx =y-2
cosx=(y-2)/(y-1)=(y-1-1)/(y-1)=1- 1/(y-1)
-1≤cosx<1
-1≤(y-2)/(y-1)<1
(y-2)/(y-1) -1<0 (y-2-y+1)/(y-1)<0-1/(y-1)<0y-1>0y>1
(y-2)/(y-1)+1≥0(y-2+y-1)/(y-1)≥0(2y-3)/(y-1)≥0 y≥3/2或y<1
综上,得y≥3/2 ,函数的值域为[3/2,+∞).