How to use feather effect on just one edge

Hello,

I would like to know how to make a feather just on one edge of the vecto shape.

I would like to have the same effect as done here:

I need it because I would like to use the same with my letters, I found this in freepik. Here is this case in illustrator file (Dropbox - what effect used.ai )

So, my question is: How was this effect done?

Thank you for any help!