Question

Fie functiile f,g:R->R, f(x)=xpatrat-x+1 si g(x)=x+4.Sa se calculeze coordonatele punctelor de intersectie a graficelor functiilor f si g.

Answer 1

[tex]\text{ Trebuie rezolvata ecuatia } f(x)=g(x)\\ x^2-x+1=x+4\Leftrightarrow \\ x^2-2x-3=0,\ \Delta=4+12=16,\\ \ x_1=\frac{2+4}{2}=3,\ x_2=\frac{2-4}{2}=-1\\ \text{ Cele doua solutii reale reprezinta abscisele celor doua }\\ \text{puncte de intersectie}.\\ f(3)=g(3)=7,\ f(-1)=g(-1)=3\\ \Rightarrow\ \boxed{G_f\cap G_g=\{A(3,7),B(-1,3)\}}[/tex]