Problem K. 203. (February 2009)
K. 203. Given that for all x0, 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