I am given this problem as extra credit in my class:
Propose TWO example recurrences that CANNOT be solved by the Master Theorem.
Note that your examples must follow the shape that $T(n) = aT(n/b) +f(n)$, where $n$ are natural numbers, $a\geq 1$, $b > 1$, and $f$ is an increasing function.
In other words, you can not give examples by making $n \leq 0$, $a < 1$, or $b \leq 1$.
Explain why your recurrences cannot be solved by the master theorem.
I can come up with ones that can't be solved but they don't follow the guidelines stated, like $a$ and $b$ being greater than $1$ or $n$ being a natural number.