Here is a complete solution that works at least with
sudo nano /etc/dhcp/dhclient.conf
# add next line (alternatively you can use append instead of prepend)
prepend domain-name "example.com other.example.com";
# before: request subnet-mask...
If you're on any sort of "professional" network that has its own DNS servers and/or if you've setup your own DNS service(s) on said network and also on your workstation, then, you might also want to comment-out this line:
# domain-name, domain-name-servers, domain-search, host-name,
--Doing so lets you use your own domain-name-servers, enabling your personalized domain-search to work much more smoothly, which is probably better than using whatever somebody else has setup for you. E.G.: I'm on the network 192.168.10.0; the company has name server 192.168.10.10 and 192.168.10.11 -- but, I run my own name server with a more extensive list of names on 192.168.10.20 (which will forward to 192.168.10.10 and .11 as needed). All my network configurations declare 192.168.10.20 and 18.104.22.168 and 22.214.171.124 (the Google name servers), but, DHCP will tend to override that preference, feeding me 192.168.10.10 as the default server. In the end... not requesting those aspects from DHCP makes for a much better network life.
Now restart the networking:
sudo /etc/init.d/networking restart