Need to figure out the syntax on a trigger when a new record is inserted

I have a table in SQL Server.  That contains 2 fields the Diagnosis code and the HCC Code.  The HCC Code is based on the Diagnosis Code and I have another database on the same server that has a lookup table for every Diagnosis code and the HCC Code.  I'm trying to set up an insert trigger that will update the HCC Field depending on what is entered in the Diagnosis but my Syntax isn't working

CREATE TRIGGER hvvmgrpt.dbo.T_hcc
   ON  hosp_hcc
   AFTER INSERT
AS 
BEGIN
	-- SET NOCOUNT ON added to prevent extra result sets from
	-- interfering with SELECT statements.
	SET NOCOUNT ON;
	update set HCC = get_HCC(Select I.diag from inserted I)
    -- Insert statements for trigger here

END
GO

CREATE FUNCTION [dbo].[GET_HCC]
(
	-- Add the parameters for the function here
	@ICD as varchar(20)
)
RETURNS Varchar(10)
AS
BEGIN
	-- Declare the return variable here
	DECLARE @result varchar(10)

	-- Add the T-SQL statements to compute the return value here
	Set @result = (SELECT a.hcc from hccsql.dbo.hcc a where left(a.icd9,3) = left(@icd,3))

	-- Return the result of the function
	RETURN @result

END