$\begingroup$

Is there a continuous function from $\mathbb{R}\to\mathbb{R}$ that reaches all of its possible values (each value in it's range) exactly $2$ times (for example, $x^2$ would be perfect if it wasn't for $0$..). Also, the same question but $3$ times.

I'm almost certain that there aren't such functions but who knows haha maybe there are a bunch...

Answers