Say that we have the function $$ f(n)=kn, \, k>0 $$ does that imply the following? $$f(n) \in O(n), \, f(n) \in \Theta(n) \text{ and } f(n) \in \Omega(n)$$ I'm fairly new to these notations and am wondering if a function can be "in" all three at the same time.
Thanks in advance
Yes. There's nothing preventing functions being in all three at the same time, and it's really easy to verify that your function indeed is.