Question

(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．

Answer 1

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

略