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HMMT 二月 2004 · CALC 赛 · 第 6 题

HMMT February 2004 — CALC Round — Problem 6

专题
Contest Math / 竞赛数学
难度
L3
来源
HMMT

题目详情

英文原题

  1. For x > 0, let f ( x ) = x . Find all values of x for which f ( x ) = f ( x ).
    6 2 2
解析

英文解析

  1. For x > 0, let f ( x ) = x . Find all values of x for which f ( x ) = f ( x ).
    Solution: 1
    ′ ′
    Let g ( x ) = log f ( x ) = x log x . Then f ( x ) /f ( x ) = g ( x ) = 1 + log x . Therefore
    ′
    f ( x ) = f ( x ) when 1 + log x = 1, that is, when x = 1.
    6 2 2