题目内容
(本小题满分12分) 设a > 1,函数
.
(1)求
的反函数
;
(2)若
在[0,1]上的最大值与最小值互为相反数,求a的值;
(3)若
的图象不经过第二象限,求a的取值范围.
【答案】
解:(1) 由![]()
∴ ![]()
∴
··································································· 4分
(2) ∵ a > 1 ∴
在[0,1]上递增
∴
,![]()
∴
即
∴
······························································································· 8分
(3)
在y轴上的截距为![]()
![]()
要使
的图象不过第二象限,
只需![]()
∴
∴ ![]()
因此,a的取值范围为
····································································· 12分
【解析】略
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