Final answer:
The correct command to backup the 'mydatabase' using pg_dump and direct the output to a file is 'pg_dump mydatabase >'. The '>' character is for output redirection to a file.
Step-by-step explanation:
The correct command to generate a database backup file of the mydatabase database and to recreate the database in the same state that it was at the time of the dump is:
pg_dump mydatabase > backupfile.sql
Therefore, the correct choice from the options provided is C) pg_dump mydatabase >. This command will invoke the pg_dump utility, which is used to backup a PostgreSQL database. It will dump the contents of mydatabase into a file named backupfile.sql or any other filename you specify after the > sign. The > character is used to redirect the output of the command into a file.