SQL list of all the user defined functions in a database

I am looking for a SQL query that outputs the function definitions for all of the user defined functions in a database catalog.

I have found as far as

SELECT OBJECT_DEFINITION (OBJECT_ID(N'dbo.UserFunctionName')) AS [Object Definition]

and

SELECT ROUTINE_NAME FROM information_schema.routines WHERE routine_type = 'function'

but I can't think of or find a way to feed the ROUTINE_NAME list to the OBJECT_ID.

The purpose here is a searchable text of the user defined function definitions in a database for database change analysis, if something like a full SQL procedure or purposed helper program is easier, I will do that and post it.

SELECT name, definition, type_desc 
  FROM sys.sql_modules m 
INNER JOIN sys.objects o 
        ON m.object_id=o.object_id
WHERE type_desc like '%function%'

You could use a CTE:

with functions(routine_name) as 
  (SELECT ROUTINE_NAME FROM information_schema.routines WHERE routine_type = 'function')
select 
  OBJECT_DEFINITION(OBJECT_ID(routine_name)) AS [Object Definition] 
from 
  functions

SELECT O.name, M.definition, O.type_desc, O.type
FROM sys.sql_modules M
INNER JOIN sys.objects O ON M.object_id=O.object_id
WHERE O.type IN ('IF','TF','FN')

Similar to this solution: Query to list all stored procedures

SELECT * 
  FROM DIDS0100.INFORMATION_SCHEMA.ROUTINES
 WHERE ROUTINE_TYPE = 'FUNCTION' 
    AND LEFT(ROUTINE_NAME, 3) NOT IN ('fn_')