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Do you know the domain and rain for cot?

So if this is cot(3x), then 3x cannot equal n*pi. Now solve for x

do I solve for x by setting 3x = 0?

Yep. Exactly what I said. ;)

Ok, but how do I get the domain or range from that?

Take the domain of the basic function and think of it geometrically.

|dw:1350961916817:dw|
Here is -cotx

|dw:1350962021979:dw|

That compression will move the asymptotes, like an accordion, toward the origin.