Let $f(n) = (n + log_2(a))^b$ and $g(n) = n^b$, for any real constants $a$ and $b$, where $b > 0$
a) Using definition of $Ω$ and $g(n)$, establish the lower bound of $f(n)$. Find the values of positive constant $c$ and non-negative integer $n_0$.
b) Using definition of $O$ and $g(n)$, establish the upper bound of $f(n)$. Find the values of positive constant $c$ and non-negative integer $n_0$.
c) Using Θ, what is your conclusion for the relationship between $f(n)$ and $g(n)$? Prove or disprove your conclusion.
I can't seem to find an example of problem of this type. Does anyone know the best method for solving it? Or does anyone know of any links to relevant examples? Thanks.