To get the max backup date of the database or to check whether database is backed up or not. You can execute below script to check the last backup date.

SELECT   d.name,
         MAX(b.backup_finish_date) AS backupfinishdate
FROM     master.sys.sysdatabases d
         LEFT OUTER JOIN msdb..backupset b
         ON       b.database_name = d.name
         AND      b.type          = 'D'
GROUP BY d.name
ORDER BY backup_finish_date DESC


SELECT   d.name,
         MAX(b.backup_finish_date) AS backupfinishdate
FROM     master.sys.sysdatabases d
         LEFT OUTER JOIN msdb..backupset b
         ON       b.database_name = d.name
         AND      b.type          = 'L'
GROUP BY d.name
ORDER BY backup_finish_date DESC