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Hi every one. Let $f:\mathbb{R}^{*}_{+}\to\mathbb{R}$ 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...