How to use 2009-era Airport Extreme in Bridge Mode Wifi
What you are describing is a WiFi extender. EG extending your Wifi network over WiFi. The basic two things you need to know are:


No this Airport won't do that. I don't believe any will.
WiFi repeaters just (usually) don't work very well.


TheWirecutter.com has a good take on it AND recommendations here http://thewirecutter.com/reviews/best-wi-fi-extender/.