After cutting bananas up they will last for a few days if left unwrapped.
If you want to keep the cut up bananas longer than a couple days in the refrigerator you should wrap the cut up bananas tightly in plastic wrap or some aluminum foil.
Then place the cut up wrapped up bananas in a sealed container and place them in the refrigerator.
The cut up bananas when put in a sealed container and wrapped up in the refrigerator should last from 4 to 7 days before they start going bad.
If you want to keep the cut up bananas longer than 4 to 7 days you can freeze them instead and when frozen the cut up frozen bananas will last for 6 months to a year.
After cutting up bananas either eat them soon or refrigerate them to keep them from going bad.