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

发布时间：2021-02-19 21:42:45

(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．


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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

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