Prefix LIKE search and indexes issue.

Hello list,

So, I have a small query design issue and I'd like to borrow some of
your wisdom.

Let's say I  a users relation, and each user has a reversed_domain field.

id | name | reversed_domain
1    Josh      com.app
...

I then have a firefox plugin which makes request to my application
server, sending along the current URL the user is browsing. Let's say
the URL is "http://mycompany.app.com/login". The code on the app takes
this data and:
 1) Extracts the domain out of it;
 2) Reverses the domain

We then get the following string as a result: "com.app.mycompany".

I then want to find the user Josh, by reversed_domain. However, as you
can see, the strings are different, and in most cases will be. I just
want it to match the first two parts of the domain (com.app).

The following query works:

SELECT * FROM users WHERE 'com.app.mycompany' LIKE reversed_domain || %

However, it does sequential search, meaning it doesn't  use any index.

What I would like to know is, how could I make it use an index? I've
done some research and asked around #postgres but things are still not
clear to me. Some good souls hinted me at the prefix extension, but
how would I use it? Is there any other simpler / extension-free way to
solve this issue?

Thanks in advance,

Marcelo.