Question

若f(x)是定义在R上的奇函数且f(x+2)=f(x),当x属于（0，1）时，f(x)=2^x-1,则f(log1/2 6)的值

Answer 1

log1/2(6)=-log2(6)>-log2(8)=-3

所以有2-log2(6)>2-3=-1
log2(6)-2<1
f[log2(6)-2]=2^[log2(6)-2]-1=2^log2(6)/2^2-1=6/4-1=1/2
f(x)是奇函数,有f[log2(6)-2]=-f[2-log2(6)]=1/2
故有f[log1/2(6)]=f(-log2(6))=f(2-log2(6))=-1/2

追问

f(-log2(6))=f(2-log2(6))是什么意思

追答

f(x)=f(2+x)

Answer 2

f(log1/2 6)=f(-log2 6)=f{(-log2 2)-(log2 3)}=f(-1-log2 3)=f(2-1-log2 3)=f(1-log2 3)=2^-log2 3=1/3