若奇函数f(x)(x∈R)满足f(3)=1,f(x+3)=f(x)+f(3),则f(32)等于()A.0B.1C.12D.-12-数学

题目简介

若奇函数f(x)(x∈R)满足f(3)=1,f(x+3)=f(x)+f(3),则f(32)等于()A.0B.1C.12D.-12-数学

题目详情

若奇函数f(x)(x∈R)满足f(3)=1,f(x+3)=f(x)+f(3),则f(
3
2
)
等于(  )
A.0B.1C.
1
2
D.-
1
2
题型:单选题难度:偏易来源:不详

答案

∵f(x+3)=f(x)+f(3),
令x=-class="stub"3
2
,则f(-class="stub"3
2
+3)=f(-class="stub"3
2
)+f(3),
即f(class="stub"3
2
)=f(-class="stub"3
2
)+f(3),
∴f(class="stub"3
2
)=class="stub"1
2

故选C.

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