Sometimes your friends who appear offline in yahoo messenger may not be actually offline,they may in the 'Invisible' mode.This maybe if they are trying to ignore you or are too busy to talk to anyone.If you want to know that she/he is visible or not, then you can use some of the trick to find the truth.
All the you need for this trick is a little bit of patient. Firstly open Yahoo! Messenger main window and double click the username of the person that you want to check. Now you should see the chat window (obviously).
Then click IMVironment button, select See all IMVironments, select Yahoo! Tools orInteractive Fun, and click on Doodle. After loading the Doodle IMVironment, there might be two possibilities. If the Doodle area will show "waiting for your friend to load Doodle" continuously which is mean the user is offline but if the user is online (invisible) the Doodle ares will load a blank page.
For the second method, double click the user to open chat window and invite the user for a voice conference. This is done by clicking on the "conference' button on the top of the chat window. If the talk button appears and turns green then that person is online.But if you receive the message 'Voice chat could not be started ' then the person is offline.
you're also can visit a few sites to check the users in invisible mode or not just by a single click, so here are the list of websites which can help you to check whether the user is online or invisible for free:
1 - 4invisible.com
2 - Xeeber.net
3 - Invisible-Scanner.com
4 - Imvisible.info
5 - Yahooscan.net
6 - Detectinvisible.com
7 - Invisible.ir
8 - Ydetect.com
Actually there are a lot of other website that can help you check whether your friend is online or not, but the list above is the top site to check the visibility of your friend.