Re: [中學] 函數相關

看板Math作者Tiderus (修煉人生)時間10年前 (2015/12/11 22:15)推噓4(4推 0噓 13→)

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※ 引述《ilovecurl (ilovecurl)》之銘言： : Suppose that a,b and c are non-zero real numbers. : Define h(x)=(ax+b)/(bx+c) for x≠-c/b. : Determine all triples (a,b,c) for which h(h(x))=x : for every real number x with x≠-c/b and h(x)≠-c/b : 這題是學生問的問題,不過沒有解答,本身思路是以反函數的考量下去解的 : 但自己算的不算很有把握,所以上來求教 : 是否有大大能夠提供比較有把握的解答可供參考,謝謝! 不算有把握，就是試試看XD 設y=h(x)=(ax+b)/(bx+c) (ay+b)/(by+c) = x => y = (b-cx)/(bx-a) (ax+b)/(bx+c) = (b-cx)/(bx-a) => y = (a+c)x/(a+c) 〔加比〕= x 〔若a+c≠0〕 (ax+b)/(bx+c) = x => bx^2 +(c-a)x -b = 0 xεR => (c-a)^2 + 4b^2 ≧0 => 咦？好像是任意實數？ (x≠-c/b and h(x)≠-c/b, a,b and c are non-zero) 其他請高手補充:) -- http://attachment.van698.com/forum/201511/30/225019fywnza6atswsh36t.gif

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迷途中唯一的導航是對自己誠實 -- ※ 發信站: 批踢踢實業坊(ptt.cc), 來自: 123.240.91.95 ※ 文章網址: https://www.ptt.cc/bbs/Math/M.1449843302.A.0FD.html ※ 編輯: Tiderus (123.240.91.95), 12/11/2015 22:39:21

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