推 ericakk :感謝您~一目了然! ^^ 05/10 23:24
※ 引述《ericakk (ericakk)》之銘言：
: 設函數f具有以下性質:
: 對於所有正實數x皆滿足 f(3x)= 3f(x) 且f(x)= 1－|x－2| (1≦x≦3)
: 試求 滿足 f(x)= f(2010)的最小x值為何？
: Ans:420，請問該如何下筆.....先說聲謝謝喔^^
f(x) = 1-(2-x) = -1+x, 1<=x<=2
= 1-x+2 = 3-x, 2<=x<=3
0 <= f(x) <= 1
2010 = 729*a
a = 2010/729 = 2.75...
f(2010)=3f(2010/3)=9f(2010/9)=...=729f(2010/729)
=729f(a)=729(3-a)=2187-2010=177
since 0<=f(x)<=1
177=243*f(n/243)=243*(-1+x) or 243(3-x)
-1+x=177/243, or 3-x=177/243
x=n/243=177/243+1, or x=n/243=3-177/243
n=177+243=420, n=729-177=552
--
※ 發信站: 批踢踢實業坊(ptt.cc)
◆ From: 123.194.224.241