For what s/\s+$// does, see perlop and perlre, and compare that with chomp.

Is the $f =~ s/\s+$// ; statement doing the chomp function?

In this context, it's probably accomplishing more or less what the chomp would have been intended to accomplish. There are however technical differences, e.g., the + causes the substitution to remove as much trailing whitespace as it can find, so if the line ends with twenty-seven spaces in a row followed by three tab characters, a carriage return, and a line feed, they'll all be taken off; chomp would probably only take the CRLF, or maybe even just the linefeed, depending on the value of $/.

For more details about the substitution, read the chapter on regular expressions in your favorite Perl book. Don't worry too much about chomp for now (until you have been using Perl for a while longer); if you know how to use s///, you can probably get by without chomp for the time being. (Regular expressions, on the other hand, are pretty much impossible to live without. The internet as we know it could more likely exist without integrated circuits than without regular expressions.)