Question

(本小題滿分12分) 設a > 1，函數．
（1）求的反函數；
（2）若在[0，1]上的最大值與最小值互為相反數，求a的值；
（3）若的圖象不經過第二象限，求a的取值范圍．

Answer 1

解：(1) 由
∴
∴··································································· 4分
(2) ∵ a > 1  ∴在[0，1]上遞增
∴，
∴   即    
∴······························································································· 8分
(3) 在y軸上的截距為

要使的圖象不過第二象限，
只需
∴     
∴
因此，a的取值范圍為····································································· 12分

略