You can use the dm_exec_function_stats (in SQL Server 2016) to check detailed execution details of a function. These include:
execution_count - the number of times this function has been executed
last_execution_time - how long did the function take to execute
Here is a nice example of using dm_exec_function_stats
SELECT
DB_NAME(database_id) AS DBName,
OBJECT_SCHEMA_NAME(OBJECT_ID, database_id) + '.' + OBJECT_NAME(OBJECT_ID, database_id) AS FName,
STATS.execution_count,
STATS.total_elapsed_time / STATS.execution_count AS ElapsedTime,
STATS.last_execution_time,
STATS.max_worker_time,
STATS.max_physical_reads,
STATS.max_logical_reads,
STATS.max_logical_writes,
TEXT.Text
FROM sys.dm_exec_function_stats STATS
CROSS APPLY sys.dm_exec_sql_text(sql_handle) TEXT
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