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Function: driver
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Cacher.php
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Function: initiateCache
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/controllers/ver3/Contents.php
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Function: _error_handler
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: model
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/application/libraries/Common.php
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Function: getFloatingMyInfo
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Line: 559
Function: get_footer
File: /volume1/web/PhpstormProjects/www_polymath_co_kr/index.php
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Function: require_once
수학동아 - 폴리매스
함께 풀고 싶은 문제
창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.
디듀우
2019.09.22 03:16
조회 646
실수 전체를 정의역과 치역으로 갖는 함수 f(x)와 모든 실수 c에 대해 다음이 성립하는 f(x)의 필요충분조건을 구하시오.
(1) f(x+c)=f(x)+c
(2) f(cx)=cf(x)
(3) f(x^c)={f(x)}^c
-
(1)조건에 c=x 을 대입하면
f(2x)=f(x)+x
(2)조건에 c=2 을 대입하면
f(2x)=2f(x)
따라서 두 식을 연립하면
f(x)=x
이 식은 조건 (3)도 만족한다.
| 주어진 조건을 만족하는 함수는는f(x)=x 이다. |
-
디듀우
Lv.7
2019.09.22 18:22
4개 조건을 모두 만족하는 함수를 구하는 것이 아니라, 4개 조건 각각에 대해 필요충분조건인 함수의 성질을 구하는 것입니다. 또한 c는 임의의 실수이므로 x라고 할 수 없습니다.
좋아요0
-
아 모든 실수 c라고 적혀있어서 유한확정값이 아닌줄 알았네요.
좋아요0
지금 바로
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