I'd like to ask for the hints for part (1) and (3) in the exercise below.
I stuck completely at part (1). For part (3), I found a way to simplify $f(n)/g(n)$, but then the answer would depend on the constant $k$, and not all the conclusions about the asymptotic relationships between $f$ and $g$ could be drawn from there. So I don't think my approach is correct. Here's my working so far:
Please note that we use the following definitions of the asymptotic notations: