investigate
The French word 'enquêter' is used in the same way as the English word 'investigate'. It means to try to find out the truth about something, especially a crime or an accident. For example, 'La police enquête sur l'accident' means 'The police are investigating the accident'.
The inspector will investigate this crime
This phrase presents a future action where 'The inspector' ('L'inspecteur') will 'investigate' ('enquêter') 'this crime' ('ce crime'). The verb 'enquêter' is used to describe the action of seeking information about something, in this context, a crime.
I like to investigate unexplained phenomena
In this phrase, the speaker expresses a preference ('J'aime') for investigating ('enquêter') 'unexplained phenomena' ('des phénomènes inexpliqués'). Again, 'enquêter' is used to indicate the action of finding information about something, here referring to unexplained phenomena.
We must investigate these allegations
It's an instruction or expression of obligation where 'we' ('Nous') 'must' ('devons') 'investigate' ('enquêter') 'these allegations' ('ces allégations'). The verb 'enquêter' shows the action of searching for information, in a context of someone needing to find out more about certain allegations.