Permissions required to execute UDF Scalar Function inside a trigger
Permissions on indirectly referenced objects are not checked as long as the objects involved have the same owner. This is known as ownership chaining. Users need permission on only the object used directly (table in this case), not on the objects used by the trigger (e.g. function) as long as the ownership chain is unbroken.

One can leverage ownership chains to encapsulate functionality in views, stored procedures, triggers, and functions without granting direct permissions. 

See the Ownership Chains topic in the Authorization and Permissions in SQL Server documentation for more information.