Problem 430 (difficulty: 2/10)

In which points are the following functions continuous?

 (1)  \(\displaystyle f(x)=\begin{cases} {x} & \text{if $\frac1x\in \N$} \\ 0 & \text{if $\frac1x\not\in \N$;} \end{cases}\)      (2)  \(\displaystyle f(x)=\begin{cases} 3x+7 & \text{if $x\in \Q$} \\ 4x & \text{if $x\not\in \Q$}; \end{cases}\)      (3)  \(\displaystyle f(x)=\begin{cases} x^2 & \text{if $x\geq0$} \\ cx & \text{if $x<0$}. \end{cases}\)

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