For that example, f(x) isn't a polynomial function hence master theorem isn't applicable.
See this: https://www.quora.com/Master-Theorem-T-n-2T-n-2-%2B-n-log-n-I-thought-the-answer-would-be-%CE%98-nlogn-but-the-solution-says-the-Master-Theorem-does-not-apply/answer/Jeff-Erickson?ch=10&share=00ec8a0b&srid=3XD8D
@smsubham
Are you sure about that ?
https://en.wikipedia.org/wiki/Master_theorem_(analysis_of_algorithms)#Inadmissible_equations
read the about the 2nd case....I have used extended version of master theorem.
The equation should be in the form of $aT(\frac{n}{b}) + O(n^{k} log^{p}n)$ where $a\geq1$ and $b>1$ and $k\geq0$ and $p$ is a real number.
If you can convert the given recurrence relation in this form then you can apply master theorem.
This version is used for divide and conquer type of problems like mergesort, quicksort etc
Another version pf master theorem is used for subtract and conquer, that is when the bigger problem is like sum of smaller subproblems.
it is of the form $aT(n-b) + O(n^{k})$
The above are some cases where you can't apply master theorem.
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