Comprehensive and Detailed Explanation From BIG-IP Administration Control Plane Administration documents:

The recommended and supported method for creating BIG-IP users from the CLI is through TMSH, using the authentication subsystem.

tmsh create auth user <username> prompt-for-password:

Properly creates the user within BIG-IP's AAA/authentication framework

Encrypts the password securely

Ensures the user is stored and managed correctly in the BIG-IP configuration database

Is fully supported and documented

Why the other options are incorrect:

B is unsafe and unsupported because editing bigip.conf directly and storing clear-text passwords violates security and configuration management best practices.

C (f5adduser / f5passwd) is deprecated and not recommended for modern BIG-IP versions.

D creates a Linux system user only, not a BIG-IP administrative user, and will not allow access to the Configuration Utility or TMSH roles.