Question

已知定義在R上的函數(shù)y＝f(x)滿足下列三個(gè)條件：①對(duì)任意的x∈R都有f(x＋2)＝－f(x)；②對(duì)于任意的0≤x₁<x₂≤2，都有f(x₁)<f(x₂)；③y＝f(x＋2)的圖像關(guān)于y軸對(duì)稱．下列結(jié)論中，正確的是(　　)

A．f(4.5)<f(6.5)<f(7)

B．f(4.5)<f(7)<f(6.5)

C．f(7)<f(4.5)<f(6.5)

D．f(7)<f(6.5)<f(4.5)

Answer 1

B

由f(x＋2)＝－f(x)，得f(x＋4)＝－f(x＋2)＝f(x)，則函數(shù)y＝f(x)的最小正周期為4；根據(jù)②知函數(shù)y＝f(x)在[0，2]上單調(diào)遞增；根據(jù)③知函數(shù)y＝f(x)的圖像關(guān)于直線x＝2對(duì)稱，所以f(4.5)＝f(0.5)，f(6.5)＝f(2.5)＝f(1.5)，f(7)＝f(3)＝f(1)．故f(4.5)<f(7)<f(6.5)．