Question

determinati numerele reale a,stiind ca punctul A(a,a),apartine graficului functiei f(x)=2-x la a doua

Answer 1

$A\in G_f \ daca \ f(a)=a\\ \\ f(a)=2-a^2\\ \\ \Rightarrow a=2-a^2 \Rightarrow a^2+a-2=0 \\ \\ \Delta=1^2-4\cdot1\cdot(-2)=1+8=9\\ \\ a_{1,~2}=\frac{-b \pm \sqrt{\Delta}}{2a}=\frac{-1 \pm 3}{2}\\ \\ \Rightarrow a_1=\frac{-1-3}{2}=-2;\\ \\ a_2=\frac{-1+3}{2}=1\\ \\ \boxed{a\in \{-2;~1\}}$