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HMMT 二月 2007 · GEN2 赛 · 第 9 题

HMMT February 2007 — GEN2 Round — Problem 9

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. [ 6 ] Let A := Q \ { 0 , 1 } denote the set of all rationals other than 0 and 1. A function f : A → R hasthe property that for all x ∈ A ,
    ( )
    f ( x ) + f 1 − = log | x | .1
    Compute the value of f (2007).x
解析

英文解析

  1. [ 6 ] Let A := Q \ { 0 , 1 } denote the set of all rationals other than 0 and 1. A function f : A → R hasthe property that for all x ∈ A ,
    ( )
    f ( x ) + f 1 − = log | x | .1
    Compute the value of f (2007).x
    Answer: log ( 2007 / 2006 ) . Same as Algebra #8.