
设f(x)是定义在R上的奇函数,且f(x+2)= -f(x),当0≤x≤1时, f (x) = x,则f (7.5 ) = ( )
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∵y = f (x)是定义在R上的奇函数,∴点(0,0)是其对称中心;
又∵f (x+2 )= -f (x) = f (-x),即f (1+ x) = f (1-x), ∴直线x = 1是y = f (x) 对称轴,故y = f (x)是周期为2的周期函数。
∴f (7.5 ) = f (8-0.5 ) = f (-0.5 ) = -f (0.5 ) =-0.5
又∵f (x+2 )= -f (x) = f (-x),即f (1+ x) = f (1-x), ∴直线x = 1是y = f (x) 对称轴,故y = f (x)是周期为2的周期函数。
∴f (7.5 ) = f (8-0.5 ) = f (-0.5 ) = -f (0.5 ) =-0.5
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