函数y=log(x-1)(3-x)的定义域是( ) A.(1,2)∪(3,4) B.[1,2]∪[3,4] C.(1,2)∪(2,3) D.[1,2]∪[2,3]
问题描述:
函数y=log(x-1)(3-x)的定义域是( )
A. (1,2)∪(3,4)
B. [1,2]∪[3,4]
C. (1,2)∪(2,3)
D. [1,2]∪[2,3]
答
函数y=log(x-1)(3-x)的定义域满足:
,解得1<x<2或2<x<3.
x−1≥0 x−1≠1 3−x>0
∴函数y=log(x-1)(3-x)的定义域是(1,2)∪(2,3).
故选:C.