Path: ccsf.homeunix.org!ccsf.homeunix.org!news1.wakwak.com!nf1.xephion.ne.jp!onion.ish.org!news.heimat.gr.jp!news.jone-system.com!mmcatv.co.jp!news.moat.net!news.glorb.com!postnews1.google.com!not-for-mail
From: eurms@apionet.or.jp (M_SHIRAISHI)
Newsgroups: fj.sci.math
Subject: Re: =?ISO-8859-1?Q?Quiz=5F06iv2004_=3F=3F=3F=3F?=
Date: 17 May 2004 02:13:56 -0700
Organization: http://groups.google.com
Lines: 20
Message-ID: <800c7853.0405170113.6a4a8a01@posting.google.com>
References: <800c7853.0404130611.3be17e79@posting.google.com> <c7jvjj$llf$2@nr1.vectant.ne.jp> <800c7853.0405090219.27c25a85@posting.google.com> <c7l6k0$jg8$1@nr1.vectant.ne.jp> <c7l8br$kep$2@nr1.vectant.ne.jp> <800c7853.0405110609.451ab71f@posting.google.com> <40A1B719.2090404@slis.tsukuba.ac.jp> <800c7853.0405120521.77640259@posting.google.com> <040513132314.M0100960@flame.hirata.nuee.nagoya-u.ac.jp> <800c7853.0405161110.396a27b9@posting.google.com>
NNTP-Posting-Host: 218.230.228.238
Content-Type: text/plain; charset=ISO-8859-1
Content-Transfer-Encoding: 8bit
X-Trace: posting.google.com 1084785237 13460 127.0.0.1 (17 May 2004 09:13:57 GMT)
X-Complaints-To: groups-abuse@google.com
NNTP-Posting-Date: Mon, 17 May 2004 09:13:57 +0000 (UTC)
Xref: ccsf.homeunix.org fj.sci.math:1113

Takao Ono wrote in message news:<040517170416.M0122627@flame.hirata.nuee.nagoya-u.ac.jp>...
> ????? f(x) ???? ?(?f(x)) = -?f(x) ?????????
> ???????.


?(?x)??(x_1?x)?{x_1?(x??x}?{x_1?x}???x ?????

????? f(x) ???? ?(?f(x)) ???f(x) ???????
??????


?(?f(x)) ??{f(x??x)?f(x)}
??{f(x??x)}??f(x)
?[f{(x??x)??x}?{f(x??x)]?[f(x??x)?f(x)]
?f(x?2?x)?2f(x??x)?f(x)


# ???????????????????????

f(x)?x ??????(?x)?(x?2?x)?2(x??x)?x??  ?(???)?