Question

Se considera functiile f,g:Rcu valori in R, f(x)=2x-1 si g(x)=-4x+1. Sa se determine coordonatele punctului de intersectie a graficelor celor doua functii.

Answer 1

f(x) = 2x-1
g(x) = -4x+1

Consideram A(a,b) punctul de intersectie a graficelor celor doua functii.

A(a,b) apartine Gf => f(a) = b => 2a-1 = b
A(a,b) apartine Gg => g(a) = b => -4a+1 = b

=> 2a-1 = -4a+1 => 6a = 2 => a = 1/3;
2×1/3 - 1 = b => b = 2/3-1 => b = 2/3 - 3/3 => b = (2-3)/3 => b = -1/3

=> A(1/3,-1/3)