I would like to know if this statement is true:I thought of giving a counter example by defining: which will give us that  but i'm nut sure if it's possible to say that  beacuse I suspect that it might be right because of the definition of Big O. And if that's right that means that the counter example i gave is not good.Am i right? or the statement is true? If it's true, how am I suppose to approach such questions?
Prove/Disprove that $f(n) + g(n)= O(g(n)*f(n))$?
asymptotics;landau notation