You already know the explanations so i shortly remember the functions
1) Regulator of Currency
The monopoly of issuing notes vested in the central bank ensures uniformity in the notes issued which helps in facilitating exchange and trade within the country. It brings stability in the monetary system and creates confidence among the public.
2) Fiscal Agent and Adviser to the Government and Banker
3) Custodian of Cash Reserves of Commercial Banks
4) Set interest rates to target low inflation and maintain economic growth. Custody and Management of Foreign Exchange Reserves
5) Lender of the Last Resort
6) Controller of Credit