I have started learning concurrency and threads in Java. I know the basics of synchronized (i.e. what it does). Conceptually I understand that it provides mutually exclusive
Synchronization is usually needed when you are sharing data between multiple invocations and there is a possibility that the data would be modified resulting in inconsistency. If the data is read-only then you dont need to synchronize.
In the code snippet above, there is no data that is being shared. The methods work on the input provided and return the output. If multiple threads invoke one of your method, each invocation will have its own input and output. Hence, there is no chance of in-consistency anywhere. So, your methods in the above snippet need not be synchornized.
Synchronisation, if unnecessarily used, would sure degrade the performance due to the overheads involved and hence should be cautiously used only when required.