Question

Se considera functia f:R->R,f(x)=(a+1)a+3 ,a€R
a)aflati valorile numarului a pentru care punctul P(a,5)apartine graficului functiei f

Answer 1

[tex]f:R \rightarrow R,f(a)=(a+1)a+3\\ G_f = \{(x,f(x)):x \in R\}\\~\\~ P(a,5) \in G_f \implies f(a) = 5\\~ (a+1)a+3 = 5\\~ a^2+a-2 = 0\\~ \Delta = 1+8 = 9 = 3*3\\~ a_1 = \frac{-1+\sqrt{9}}{2} = 1\\~ a_2 = -2\\~ P_1(1,5),P_2(-2,5) \in G_f[/tex]