$\begin{align}  & f(x)=\left| x \right|\,\,\,\,,\,\,\,\,\,g(x)=\frac{x}{1-x} \\  & \Rightarrow g(\sqrt{2})=\frac{\sqrt{2}}{1-\sqrt{2}}=\frac{\sqrt{2}}{1-\sqrt{2}}\times \frac{1+\sqrt{2}}{1+\sqrt{2}}=\frac{\sqrt{2}+2}{-1}=-\sqrt{2}-2 \\  & (fog)(\sqrt{2})=f(g(\sqrt{2}))=f(-\sqrt{2}-2) \\  & =\left[ -\sqrt{2}-2 \right]=\left[ -\sqrt{2} \right]-2=-4 \\ \end{align}$