This is the 16225th most frequent Russian word.
расследованию
Investigation.
In this sentence, "расследованию" is used in the dative case, referring to the beginning of an investigation process.
Полиция приступила к расследованию сложного дела.
The police started investigating a complex case.
Here, "расследованию" is in the dative case, showing an indirect object relationship where attention is dedicated to the investigation.
Мы уделяем большое внимание расследованию всех происшествий.
We pay great attention to the investigation of all incidents.
In this sentence, "расследованию" is again in the dative case, indicating relevance or relation to the investigation.