Which network server is malfunctioning if a user can ping the IP address of a web server but cannot ping the web server host name?

When a user can successfully ping the IP address of a web server but cannot ping the web server's hostname, this indicates a problem with the server responsible for name resolution. In this case, the correct answer is the DNS server.

Domain Name System (DNS) servers translate hostnames (such as www.example.com) into IP addresses that computers use to identify each other on the network. Since the user is able to reach the web server via its IP address, it confirms that the web server is active and responsive. However, the failure to ping the hostname suggests that the DNS server is unable to resolve the hostname into its corresponding IP address.

By contrast, a DHCP server manages IP address distribution and would not directly affect hostname resolution. An FTP server serves files over the network, which again would not involve hostname resolution issues. A Proxy server acts as an intermediary for requests from clients seeking resources from other servers and is not involved in converting hostnames to IP addresses either.

Thus, the inability to ping the web server by its hostname points specifically to a malfunction or failure of the DNS server's capability to resolve that hostname.