[tex]\it f(x)=\dfrac{x-4}{x^2+2} \\ \\ \\ Gf\cap Ox=A(x,\ 0) \Rightarrow f(x)=0 \Rightarrow x-4=0 \Rightarrow x=4 \Rightarrow A(4,\ 0)\\ \\ \\ Gf\cap Oy = B(0,\ y) \Rightarrow f(0)=y \Rightarrow \dfrac{-4}{2} =y \Rightarrow y = -2 \Rightarrow B(0,\ -2)\\ \\ \\ AB^2=(x_B-x_A)^2+(y_B-y_A)^2 =4^2+(-2)^2=16+4=20\\ \\ \\ AB=\sqrt{20}=\sqrt{4\cdot5}=2\sqrt5[/tex]
