Thanks for the question. I understand you are experiencing issues with your function keys. The following resource may help to resolve your issue:
If you continue to have issues, try an SMC and NVRAM reset:
I have a similar problem. After an upgrade to Mavericks, the function keys no longer work, or they are mapped differently. I have checked settings, and they are all different. My keyboard is pretty old, but it is the wireless aluminium one which seems to correlate to the up-to-date picture on apple -- How to identify keyboard localizations
So, is the answer quite simply my keyboard has been superseded?