Question

已知函数y=f(x)是偶函数，y=f(x-2)在【0,2】上单调递减则：A f(0)<f(-1)<f(2) B f(2)<f(-1)<f(0)

Answer 1

已知函数y=f(x)是偶函数，y=f(x-2)在【0,2】上单调递减则：A f(0)<f(-1)<f(2) B f(2)<f(-1)<f(0)
解析：∵函数y=f(x)是偶函数，∴f(x)关于Y轴对称
∵y=f(x-2)在【0,2】上单调递减，其图像是f(x)图像水平右移2个单位
∴f(x)图像在[-2,0]上单调减，在【0,2】上单调递增
∴f(0)<f(-1)<f(2)成立
选择A

Answer 2

0<=x<=2,
-2<=x-2<=0.
f(x)在[-2,0]上单调递减. f(-1)>=f(0), 所以,B不对.
f(x)在[0,2]上单调递增. f(0)<=f(1)<=f(2). f(0)<=f(1)=f(-1)<=f(2). A对.