a given function and $g:\mathbb{R}^2\to\mathbb{R}^2$ the function defined by:

$$g(x,y)=\begin{cases}

(x,y) & \text{if $x\leq 0$}\\

(x,y+f(x)) & \text{if $x>0$}

\end{cases}$$

Questions: What is the condition on $f$ for:

1) The continuity of $g$ in $\mathbb{R}^2$?

2) The differentiability of $g$ in $\mathbb{R}^2$? Thank you[FONT="]

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