수학동아 - 폴리매스

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Function: get_footer

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Function: require_once

함께 풀고 싶은 문제

창의력을 기를 수 있는 수학 문제 또는 퍼즐을 내는 곳입니다.

[창의 퍼즐] [HME] 함수 f(x)

은총알 2020.01.22 09:19 조회 693

문제 푼 사람 0명

페이스북 트위터 카카오톡 카카오스토리 네이버블로그 네이버밴드

HME 수학학력평가 2014년도 하반기 23번입니다.

함수 f(x)는 다음 두 조건을 만족한다.

___________________________________________________________________________

(가) f(1)= $\frac{7}{3}$

(나) f(x)= $\frac{1+f(x+3)}{1-f(x+3)}$

____________________________________________________________________________

f(1000)= $\frac{b}{a}$ 일 때, a+b의 값을 구하여라. (단, a, b는 서로소)

이전글 [HME] 교점의 개수

다음글 함수

이 문제 어떠셨나요?

글쎄요

어려워요

문제 찜하기 목록보기

댓글 작성하기

은총알 Lv.11 2020.01.22 09:19 비밀댓글

비밀 댓글이 등록 되었습니다.

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다시 도전

도전

로보카폴리 Lv.11 2020.01.22 09:27 비밀댓글

비밀 댓글이 등록 되었습니다.

댓글 작성하기 댓글수1
- 은총알 Lv.11 2020.01.22 09:40
  
  앗.. 문제 오류 수정했습니다!
  
  좋아요0
로보카폴리 Lv.11 2020.01.22 09:46

(가) 조건에 의해 f(1)=7/3 이고 이를

(나) 조건에 x=1을 대입하여 식을 세우며

1+f(4)/1-f(4)=7/3 ,3+3*f(4)=7-7*f(4)

11*f(4)=4 f(4)=4/11

마찬가지로 (나) 조건에 f(4)를 대입하면

1+f(7)/1-f(7)=4/11 , 11+11*f(7)=4-4*f(7)

15*f(7)=-7 f(7)=-7/15 ??

댓글 작성하기 좋아요0 댓글수1
- 은총알 Lv.11 2020.01.22 09:49
  
  비댓, 정답확인요청!!
  
  좋아요0

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