xargs provides an optin --arg-file. With -L1 option to treat each line as argument, the simplest command we can make is as follows

$ xargs -L1 --arg-file=ip-addr.txt dig +short -x
google-public-dns-a.google.com.
resolver2.opendns.com.

If it's necessary to display the IP address next to the resolved domain, we can also do:

$ xargs -L1 --arg-file=ip-addr.txt sh -c 'printf "%s: " "$1"; dig +short -x "$1"' sh
8.8.8.8: google-public-dns-a.google.com.
208.67.220.220: resolver2.opendns.com.

Of course, xargs is an extra process. What if we wanted to only use shell and dig ? With bash version 4 and over, we can use mapfile or readarray to get lines of the text file into array, and then process items in a loop:

$ mapfile -t -d $'\n' < ip-addr.txt
$ for i in "${MAPFILE[@]}" ; do printf "%s:" "$i"; dig +short -x "$i"; done
8.8.8.8:google-public-dns-a.google.com.
208.67.220.220:resolver2.opendns.com.

If the IP addresses are few and don't require a long text file, POSIXly, we could use set to define values as positional parameters:

$ set -- 8.8.8.8 208.67.220.220
$ for i ; do printf "%s:" "$i"; dig +short -x "$i"; done
8.8.8.8:google-public-dns-a.google.com.
208.67.220.220:resolver2.opendns.com.

We can also use dig -x $IP_ADDRESS +short in a script like so:

#!/bin/bash
export LC_ALL=C
# without specifying 'in' part, bourne-like shells default
# to iterating over positional parameters
for item
do
     domain=$(dig -x "$item"  +short)
     # this logic can also be reversed with
     # [ "x$domain" = "x" ] && echo "empty" || echo "$domain"
     if [ -n "$domain"  ] ;
     then
         echo "$domain"
     else
         echo "$item" result is NULL
     fi
done

Demo of sample usage(all ip addresses given as space separeted):

$ ./reverse_dns_lookup.sh 8.8.8.8 74.125.193.94 151.101.193.69                 
google-public-dns-a.google.com.
ig-in-f94.1e100.net.
151.101.193.69 result is NULL

As you can see , in the last example our DNS server didn't find domain for the ip address we gave it. In such case we can use a different DNS server, for instance open_dns with dig @208.67.220.220 $IP_ADDRESS +short

In the demo above, the ip addresses are provided on command line, like ./reverse_dns_lookup.sh ADDRESS1 ADDRESS2 ADDRESS2 but you also can use a file for that, like so:

$ cat ip_addresses.txt |  xargs ./reverse_dns_lookup.sh                          <
google-public-dns-a.google.com.
resolver2.opendns.com.
192.30.253.112 result is NULL

Alternative script version:

Here's alternative version of the script that prints the AUTHORITY section from dig's output. This may be much better and more reliable than just +short version. NOTE: this uses 8.8.8.8 , which is Google's public DNS. Use a different server if you feel necessary.

#!/bin/bash
export LC_ALL=C
for item
do
 domain=$(dig @8.8.8.8  -x "$item" +noall +authority +answer)
 if [ -n "$domain"  ] ;
 then
     echo "$domain"
 else
     echo "$item" result is NULL
 fi
done

Demo:

$ cat ip_addresses.txt |  xargs ./reverse_dns_lookup.sh 

; <<>> DiG 9.10.3-P4-Ubuntu <<>> @8.8.8.8 -x 8.8.8.8 +noall +authority +answer
; (1 server found)
;; global options: +cmd
8.8.8.8.in-addr.arpa.   21390   IN  PTR google-public-dns-a.google.com.

; <<>> DiG 9.10.3-P4-Ubuntu <<>> @8.8.8.8 -x 208.67.220.220 +noall +authority +answer
; (1 server found)
;; global options: +cmd
220.220.67.208.in-addr.arpa. 6674 IN    PTR resolver2.opendns.com.

; <<>> DiG 9.10.3-P4-Ubuntu <<>> @8.8.8.8 -x 192.30.253.112 +noall +authority +answer
; (1 server found)
;; global options: +cmd
253.30.192.in-addr.arpa. 10 IN  SOA ns1.p16.dynect.net. ops.github.com. 6 3600 600 604800 60