I have one web serber which has IIS 8.5 installed on it.In this server an application is deployed which authenticates users and on the basis of user market , application specific to that market is shown in the browser. There will be multiple markets and
each market will have application server. User can only access web server , application servers are not accessible through internet.All the requests will follow user->web server->application server path.

Refer diagram
Suppose user hits x.com then user will be authenticated using login application(MVC) deployed on web server.On the basis of user market application is chosen.There are three market and first application is selected which is deployed in IIS8.5 and only accessible
internally. These applications are MVC application .

User should see x.com only not a.com/b.com/c.com. My problem is how to do this in IIS / MVC application.

Instead of making a.com/b.com/c.com can you put everything under x.com (using areas). If you can do this then you can use routing to route the request.