推 wa007123456 :謝謝你 可是我看不懂 囧 08/14 11:51
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→ wa007123456 :inverse 是指反函數嗎? 08/14 11:53
※ 引述《wa007123456 (大笨羊)》之銘言：
: 大家好! 以下是題目
: ==============================================
: a為101^x+x-5=0之一根 b為log<101>(x)+x-5=0 之一根
: 求a+b (log<x>表示以x為底數)
: =============================================
: 感謝回答><
denote f(x) = 101^x
denote f inverse as f^
a = f^f(a) = f^(-a+5)
denote u = -a + 5
-u + 5 = f^(u)
f^(b) = -b + 5
however, f^(x), x are both strictly increasing
hence, f^(x) + x is strictly increasing
then f^(x) + x = 5 has a unique solution
then u = b
then - a + 5 = b
a + b = 5
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