Why is the schema prefix (dbo) mandatory when we call a function?
Then why we can call function without prefix (schema), created under dbo?


From Books Online Document on UDF's 


  Scalar-valued functions can be invoked where scalar expressions are used. This includes computed columns and CHECK constraint definitions. Scalar-valued functions can also be executed by using the EXECUTE statement. Scalar-valued functions must be invoked by using at least the two-part name of the function. 


So this is basically a restriction set by SQL Server development team and I consider it quite correct. Even if it is somehow allowed (just for sake of conversation) I would still use Schema prefix.

I always support using schema name even if it would work without adding it. This is best practice and all "Good" developers use it no matter how much redundant it is.

The other reason what I see is, Database engine needs something to differentiate between system function like getdate () and user defined functions. If you are allowed to call function without schema name how would database engine differentiate between User created function named Getdate or system GETDATE() function.