问题标题:
函数y=log12(x2−1)−−−−−−−−−−−√的定义域为()。A.(−2√,−1)∪(1,2√)B.(−2,1)∪(1,2)C.[−2,−1)∪(1,2]D.[−2√,−1)∪(1,2√]
问题描述:
函数y=log12(x2−1)−−−−−−−−−−−√的定义域为( )。A.(−2√,−1)∪(1,2√)B.(−2,1)∪(1,2)C.[−2,−1)∪(1,2]D.[−2√,−1)∪(1,2√]
刘椿年回答:
本题主要考查函数的概念与图像。由复合函数定义域解法,知y=log12(x2−1)−−−−−−−−−−−√函数的定义域满足x2−1>0,log12(x2−1)⩾0即0<x2−1⩽1,解得x∈[−2√,1)∪(1,2√]。即函数y=log12(x2−1)−−−−
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