UPPER

DROP TABLE t1 cascade constraints purge;
CREATE TABLE t1 (
  id INT,
  usr_name varchar2(30) NOT NULL,
  pad varchar2(2000) DEFAULT lpad('x', 2000, 'x') NOT NULL,
    CONSTRAINT t1_pk PRIMARY KEY (id)
);

EXEC dbms_random.seed(0);

INSERT INTO t1 (id, usr_name)
SELECT
  rownum,
  dbms_random.string('a', 15)
FROM
  dual
CONNECT BY level <= 10000
;

CREATE INDEX t1_indx ON t1(id, UPPER(usr_name));
--create index t1_indx on t1(upper(usr_name));

EXEC dbms_stats.gather_table_stats(NULL, 't1', method_opt=>'for all columns size 1')

EXPLAIN plan FOR SELECT * FROM t1 WHERE id BETWEEN :1 AND :2 AND usr_name = :1;
SELECT * FROM TABLE(dbms_xplan.display);

/*
explain plan for select * from t1 where usr_name = :1;
select * from table(dbms_xplan.display);

explain plan for select * from t1 where usr_name = upper(:1);
select * from table(dbms_xplan.display);

explain plan for select * from t1 where upper(usr_name) = :1;
select * from table(dbms_xplan.display);
*/

/*
Plan hash value: 3418820351

----------------------------------------------------------------------------------------------
| Id  | Operation                            | Name  | Rows  | Bytes | Cost (%CPU)| Time     |
----------------------------------------------------------------------------------------------
|   0 | SELECT STATEMENT                     |       |     1 |  2021 |    18   (0)| 00:00:01 |
|*  1 |  FILTER                              |       |       |       |            |          |
|*  2 |   TABLE ACCESS BY INDEX ROWID BATCHED| T1    |     1 |  2021 |    18   (0)| 00:00:01 |
|*  3 |    INDEX RANGE SCAN                  | T1_PK |    45 |       |     2   (0)| 00:00:01 |
----------------------------------------------------------------------------------------------

Predicate Information (identified by operation id):
---------------------------------------------------

   1 - filter(TO_NUMBER(:2)>=TO_NUMBER(:1))
   2 - filter("USR_NAME"=:1)
   3 - access("ID">=TO_NUMBER(:1) AND "ID"<=TO_NUMBER(:2))
*/