若奇函数f(x)满足f(3)=1,f(x+3)=f(x)+f(3),则f(3/2)=
问题描述:
若奇函数f(x)满足f(3)=1,f(x+3)=f(x)+f(3),则f(3/2)=
答
f(3)=1,f(x+3)=f(x)+f(3)
所以f(x+3)=f(x)+1
令x=-3/2
f(3/2)=f(-3/2)+1
奇函数则f(3/2)=-f(3/2)+1
f(3/2)=1/2