Get list of functions used in a view
Views are implemented as table plus rewrite rule in Postgres. Details in the manual, chapter Views and the Rule System.

The tricky part: not the view itself depends on involved functions, only the rewrite rule does. So this query should be your solution:

SELECT r.ev_class::regclass AS view, d.refobjid::regprocedure AS function
FROM   pg_rewrite r
JOIN   pg_depend  d ON d.objid = r.oid 
                   AND d.refclassid = 'pg_proc'::regclass  -- only functions
WHERE  r.ev_class = 'v123'::regclass;  -- name of view here (optionally schema-qualified)


Returns all user-defined functions (excluding built-in functions).

The query assumes you did not define any additional rules for the view. Else filter the one with rulename = '_RETURN', which is the default name for the rewrite rules of a view.

The cast to regprocedure (not just regproc) returns the function with argument types, uniquely identifying it. The name is schema-qualified automatically if the current search_path would not resolve differently otherwise.