Onto from a Parabola Piece
Difficulty: Medium · Topics: Algebra, Functions, Properties of Functions
Parabola bo‘lagidan syuryektiv
The function f:[1, 4]→[m, n], f(x)=x^2-4x+1, is onto . Its graph is shown.
graph "x":[-0.5,5],"y":[-4,2],"xTicks":[1,2,3,4,5],"yTicks":[-4,-3,-2,-1,1,2],"grid":true,"clip":true,"label":"Piece of the parabola y = x^2 - 4x + 1 for 1 ≤ x ≤ 4","items":["type":"curve","points":[[1,-2],[1.071,-2.138],[1.143,-2.265],[1.214,-2.383],[1.286,-2.49],[1.357,-2.587],[1.429,-2.673],[1.5,-2.75],[1.571,-2.816],[1.643,-2.872],[1.714,-2.918],[1.786,-2.954],[1.857,-2.98],[1.929,-2.995],[2,-3],[2.071,-2.995],[2.143,-2.98],[2.214,-2.954],[2.286,-2.918],[2.357,-2.872],[2.429,-2.816],[2.5,-2.75],[2.571,-2.673],[2.643,-2.587],[2.714,-2.49],[2.786,-2.383],[2.857,-2.265],[2.929,-2.138],[3,-2],[3.071,-1.852],[3.143,-1.694],[3.214,-1.526],[3.286,-1.347],[3.357,-1.158],[3.429,-0.959],[3.5,-0.75],[3.571,-0.531],[3.643,-0.301],[3.714,-0.061],[3.786,0.189],[3.857,0.449],[3.929,0.719],[4,1]],"start":"closed","end":"closed","type":"point","at":[2,-3],"label":"(2, −3)","anchor":"s","italic":false,"type":"guide","at":[2,-3],"to":"both","type":"guide","at":[1,-2],"to":"both","type":"guide","at":[4,1],"to":"both"]
Find m+n.
f:[1, 4]→[m, n], f(x)=x^2-4x+1 funksiya syuryektiv . Uning grafigi berilgan.
graph "x":[-0.5,5],"y":[-4,2],"xTicks":[1,2,3,4,5],"yTicks":[-4,-3,-2,-1,1,2],"grid":true,"clip":true,"label":"Piece of the parabola y = x^2 - 4x + 1 for 1 ≤ x ≤ 4","items":["type":"curve","points":[[1,-2],[1.071,-2.138],[1.143,-2.265],[1.214,-2.383],[1.286,-2.49],[1.357,-2.587],[1.429,-2.673],[1.5,-2.75],[1.571,-2.816],[1.643,-2.872],[1.714,-2.918],[1.786,-2.954],[1.857,-2.98],[1.929,-2.995],[2,-3],[2.071,-2.995],[2.143,-2.98],[2.214,-2.954],[2.286,-2.918],[2.357,-2.872],[2.429,-2.816],[2.5,-2.75],[2.571,-2.673],[2.643,-2.587],[2.714,-2.49],[2.786,-2.383],[2.857,-2.265],[2.929,-2.138],[3,-2],[3.071,-1.852],[3.143,-1.694],[3.214,-1.526],[3.286,-1.347],[3.357,-1.158],[3.429,-0.959],[3.5,-0.75],[3.571,-0.531],[3.643,-0.301],[3.714,-0.061],[3.786,0.189],[3.857,0.449],[3.929,0.719],[4,1]],"start":"closed","end":"closed","type":"point","at":[2,-3],"label":"(2, −3)","anchor":"s","italic":false,"type":"guide","at":[2,-3],"to":"both","type":"guide","at":[1,-2],"to":"both","type":"guide","at":[4,1],"to":"both"]
m+n ni toping.