Question

定义在R上的偶函数y=f(x)在[0，+∞）上递减，且f(1/2)=0，则满足f(log1/4x)＜0的x的集合为_____

Answer 1

for x ≥ 0
f(log(1/4)x ) < 0 = f(1/2)
y=f(x)在[0，+∞）上递减
=> log(1/4)x > 1/2
(1/4)x > e^(1/2)
x > 4e^(1/2)

f在R上的偶函数
f(-x) = f(x)
x < -4e^(1/2) ( solution )

f(log1/4x)＜0的x的集合
= { x| x > 4e^(1/2) or x < -4e^(1/2) }