[tex]f:\mathbb{R} \rightarrow \mathbb{R},\quad f(x) = \dfrac{x-4}{x^2+2}\\ \\ Gf \cap Ox:\quad y = 0 \Rightarrow \dfrac{x-4}{x^2+2} = 0 \Rightarrow x-4 = 0 \Rightarrow x = 4 \\ \\ \Rightarrow A(4,0) \\ \\ Gf\cap Oy: \quad x = 0 \Rightarrow y = \dfrac{0-4}{0+2} \Rightarrow y = -2 \\ \\ \Rightarrow B(0,-2) \\ \\ AB = \sqrt{(0-4)^2+(-2-0)^2} = \sqrt{16+4} = \sqrt{20} = \boxed{2\sqrt 5}[/tex]
Formula folosita:
[tex]A(x_1,y_1);\quad B(x_2,y_2) \\ \\ AB = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}[/tex]
