题目内容
定义在R上的函数f(x)满足f(-x)=-f(x),f(x-2)=f(x+2),且x∈(-1,0)时,f(x)=2x+
,则f(log220)的值为( )

A.1 | B.![]() | C.-1 | D.-![]() |
C
由f(-x)=-f(x),f(x-2)=f(x+2),可知函数为奇函数,且f(x+4)=f(x),∴函数的周期为4.∵4<log220<5,0<log220-4<1,即log220-4=log2
,
∴f(log220)=f(log220-4)=f(log2
)
=-f(-log2
),∵-1<log2
<0,∴f(log2
)=
+
=
+
=1,∴f(log220)=f(log220-4)=-f(log2
)=-1,选C.

∴f(log220)=f(log220-4)=f(log2

=-f(-log2









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