f(2/3-x)=f(x)
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f(x)是奇函数则有:f(-x)=-f(x)又:f(x+2)=f(-x)则:f(x+2)=-f(x)令x=x+2则有:f[(x+2)+2]=-f(x+2)f(x+4)=-f(x+2)又:f(2/3-x)=f(x)则:f(2/3-x)=-[-f(x)]=f(x)
咨询记录 · 回答于2023-01-14
f(2/3-x)=f(x)
f(2/3-x)=f(x),f(x)为奇函数f(2/3-x)=f(-x)=-f(x)f[3/2+(3/2+x)]=-f(3/2+x)=-[-f(x)]=f(x)即f(x)=f(3+x)所以它的周期为3
f(x)是奇函数则有:f(-x)=-f(x)又:f(x+2)=f(-x)则:f(x+2)=-f(x)令x=x+2则有:f[(x+2)+2]=-f(x+2)f(x+4)=-f(x+2)又:f(2/3-x)=f(x)则:f(2/3-x)=-[-f(x)]=f(x)