Problem C. 1093. (October 2011)
C. 1093. The value of the function f(x) for a real number x is the smallest value out of x2-4x+3, x-1 and -x+7. Determine the number of solutions of the equation f(x)=c, depending on the real parameter c.
(5 pont)
Deadline expired on November 10, 2011.
Sorry, the solution is available only in Hungarian. Google translation
Megoldás. \(\displaystyle x^4x+3=x-1\) akkor, ha \(\displaystyle x=0\) vagy \(\displaystyle x=4\), ugyanakkor \(\displaystyle x^4x+3=-x+7\) akkor, ha \(\displaystyle x=-1\) vagy \(\displaystyle x=4\). Ekkor az \(\displaystyle f(x)\) a következő: ha \(\displaystyle x<1\), akkor \(\displaystyle x-1\); ha \(\displaystyle 1\le x<4\), akkor \(\displaystyle x^2-4x+3\); ha \(\displaystyle 4\le x\), akkor \(\displaystyle -x+7\).
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A megoldások száma:
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Statistics:
292 students sent a solution. 5 points: 196 students. 4 points: 27 students. 3 points: 15 students. 2 points: 41 students. 1 point: 4 students. 0 point: 6 students. Unfair, not evaluated: 3 solutionss.
Problems in Mathematics of KöMaL, October 2011