[tex]\it f(x)=\sqrt2x-2\\ \\ Gf\cap Ox=A(x,\ 0) \Rightarrow f(x)=0 \Rightarrow \sqrt2x-2=0 \Rightarrow \sqrt2x=2 \Rightarrow \\ \\ \Rightarrow \sqrt2x=\sqrt2\cdot\sqrt2|_{:\sqrt2} \Rightarrow x=\sqrt2 \Rightarrow A(\sqrt2,\ 0)\\ \\ Gf\cap Oy = B(0,\ y) \Rightarrow y=f(0) \Rightarrow y=\sqrt2\cdot0-2 \Rightarrow y=-2 \Rightarrow B(0,\ -2)\\ \\ AB^2=(x_B-x_A)^2+(y_B-y_A)^2=(0-\sqrt2)^2+(-2-0)^2=2+4=6 \Rightarrow \\ \\ \Rightarrow AB=\sqrt6[/tex]
