Mathematical and Physical Journal
for High Schools
Issued by the MATFUND Foundation
Already signed up?
New to KöMaL?
I want the old design back!!! :-)

Problem K. 203. (February 2009)

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 pont)

Deadline expired on March 10, 2009.

Sorry, the solution is available only in Hungarian. Google translation

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


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.


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