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K. 203. Given that f\left(\frac{1}{x}\right)-3f(x)=x for all x\ne0, find the value f(2) of the function.

(6 points)

This problem is for grade 9 students only.

Deadline expired on 10 March 2009.


Google Translation (Sorry, the solution is published in Hungarian only.)

Megoldás. Felírhatjuk x=2 esetén, hogy f(1/2)-3f(2)=2, amiből

(1)f(1/2)=2+3f(2).

x=1/2 esetén f(2)-3f(1/2)=1/2. Az (1)-ben f(1/2)-re kapott eredményt ez utóbbiba helyettesítve f(2)-3(2+3f(2))=1/2, innen f(2)=-13/16.


Statistics on problem K. 203.
109 students sent a solution.
6 points:71 students.
5 points:6 students.
4 points:4 students.
3 points:1 student.
1 point:1 student.
0 point:17 students.
Unfair, not evaluated:9 solutions.


  • Problems in Mathematics of KöMaL, February 2009

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