x大于等于4则 f(x)=(2分之一)的x次方
问题描述:
x大于等于4则 f(x)=(2分之一)的x次方
x小于4 .则 f(x)=f(x+1)
则f(log下2上3) 等于多少
f(log下2上3)明显小于4
但是代入f(x+1)怎么算?
答
f(log下2上3)=f(x+1)=f(log2(3)+1)
= f(log2(3)+log2(2))
=f(log2(6))
显然log2(6)小于4
所以f(log2(6))=f(log2(6)+1)=f(log2(6)+log2(2))=f(log2(12))
显然log2(12)小于4=log2(16)
所以f(log2(12))=f(log2(12)+1)=f(log2(12)+log2(2))=f(log2(24))
此时,log2(24)大于4了
则f(log2(24))=(1/2)^log2(24)=[2^-1]log2(24)=[2^log2(24)]^-1=24^-1=1/24