Yesterday I bought Pvz to my Xbox, but it doesn't appear on my library

Is it you who purchased the game? Also, did you request this to be approved by a parent account?

Please sign in here using your father's account and check if you can see the game.

https://account.microsoft.com/billing/orders

my father bought it for me and yes, it has been approved

Hi, Gabriel! I'm sorry to hear you're having trouble playing a game on your Xbox. No worries, I'm happy to assist you with this today.

Please verify if you can see the game and if it shows as completed at this link: https://account.microsoft.com/billing/orders.

Once confirmed, click on the game's picture icon to be redirected to the Xbox website. Copy and paste the Xbox website link here so I can review it.

I'm looking forward to your response so we can sort this out.

To check and see what games you own, go to https://account.xbox.com/en-us/MyGames

This will show you the games your account has. If the game you're looking for is not your account its probably on the other account.

Also, Sleeping Dogs may have been one of the Games with Gold...so you may not have access to it if you don't have an active Xbox Live Gold sub.