Question

已知定義在R上的函數(shù)f (x)的圖象關(guān)于成中心對稱，且滿足f (x) =, f (0) = 2，則f (1) + f (2) +…+ f (2007)的值為（  ）

A．2                B．1             C．0                 D．1

Answer 1

解析： C   由已知f (x) =，又f (x) =，∴，即f (x)為偶函數(shù). 又f (x + 3) == f (x)，∴f (x)是以3為周期的函數(shù).

∴f (1) = f (1) = 1，f (2) = f (1 + 3) = f (1) = 1，f (3) = f (0) = 2，

∴f (1) + f (2)+…+f (2007) = 669 [f (1) + f (2) + f (3)] = 0.