Problem K. 203. (February 2009)
K. 203. Given that for all x
0, 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
(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:
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 solutionss.
Problems in Mathematics of KöMaL, February 2009