's already back onstage ... surprising fans at 42 Dugg's concert -- less than a week after his brother Big Jook was killed in Memphis.

The rapper pulled up at Little Caesars Arena on Friday night and dapped up 42 ... before performing his hit song "F-U" for the packed crowd.

Check out the vid ... Gotti's looking iced out with the chains and an angelic, all-white 'fit -- going about his business despite the very public tragedy he's coping with.

As we previously reported ... the Tennessee-born rapper's big brother was Saturday, Jan. 13 outside a restaurant in Memphis -- he was just 47 years old.

Remember, video started circulating online of Jook's final hours ... where he grieved with close friends and family. The shooting happened just hours after he left the event.

BJ worked with Yo Gotti closely at his label Collective Music Group though more on the business/promotion side than as an artist.

Cops still aren't sure exactly who killed Jook or why though they have a pretty big lead in the case ... posting pics of a white Ford Explorer they say may have carried his killers and offering the public a cash reward for information.

Bottom line ... we're sorry for your loss Gotti -- and happy to see you back doing what you love.