Question

Define T: \[\mathbb{R}^2\rightarrow \mathbb{R}^2 \] by \[T(\left(\begin{matrix}x_1 \\ x_2\end{matrix}\right)=\left\{ \left(\begin{matrix}x_1 \\ x^2_2/x_1\end{matrix}\right) x_1\neq0 \right\}\]
and \[\left\{ \left(\begin{matrix}0 \\ x_2\end{matrix}\right) x_1=0\right\}\]

show that there exists \[u,v \epsilon \mathbb{R}^2 \] such that t(u+v) does NOT equal t(u)+t(v)