题目

已知f(x)是偶函数,当x≥0时,f(x)=a^x(a>1),若不等式f(x)≤4的解集为[-2,2],求a

提问时间：2020-10-19

答案

when x < 0-x >0f(x) = f(-x)= a^(-x)f(x) = a^x ,x > 0= 1 ,x=0= a^(-x) ,x 0f(x) ≤4a^(x) ≤4x ≤ log(a) 4for x< 0f(x) ≤4a^(-x) ≤4-x ≤ log(a) 4ie -log(a) 4 ≤x≤ log(a) 4ie log(a) 4 = 24 = a^2a = 2...