Two mistakes.

• The first is that you think that $r contains 3 characters.

  $r contains 7 characters or 7 bytes.
  $u contains 3 characters.
  So $x contains 10 (7+3) characters.
  When concatenated with characters (is_utf8 == true), bytes are treated as characters.

  $e contains 3 characters.
  so $y contains 6 (3+3) characters.

• The second is that you think you're outputting UTF-8.

  You're outputting iso-latin-1 characters since you haven't said otherwise. You happen to mix in some UTF-8, but you silenced the message warning you of this problem.

  If you want to output something other than iso-latin-1, you do do so by using open (the pragma):

  use open qw( :std :locale );
  [download]

Update: Below is the fixed code (which was modified to output the length of the strings) and the output for a UTF-8 locale.

use open qw( :std :locale );
use Encode qw(decode is_utf8);

$r = "\xc2\xa9\xc2\xae\xe2\x84\xa2";
print "Raw \$r      : ", sprintf('%2d', length($r)), " ", $r, 
      " - ", (is_utf8($r)?"is":"is not"), " utf8\n";

$u = decode('utf8',  "\xc2\xa9\xc2\xae\xe2\x84\xa2");
print "UTF8 \$u     : ", sprintf('%2d', length($u)), " ", $u, 
      " - ", (is_utf8($u)?"is":"is not"), " utf8\n";

$x = join('', $r, $u);
print "Join(\$r, \$u): ", sprintf('%2d', length($x)), " ", $x, 
      " - ", (is_utf8($x)?"is":"is not"), " utf8\n";

$e = decode('utf8', $r);
print "Encd \$e     : ", sprintf('%2d', length($e)), " ", $e, 
      " - ", (is_utf8($e)?"is":"is not"), " utf8\n"; 

$y = join('', $e, $u);
print "Join(\$e, \$u): ", sprintf('%2d', length($y)), " ", $y, 
      " - ", (is_utf8($y)?"is":"is not"), " utf8\n";
[download]

Raw $r      :  7 ©®™ - is not utf8
UTF8 $u     :  3 ©®™ - is utf8
Join($r, $u): 10 ©®™©®™ - is utf8
Encd $e     :  3 ©®™ - is utf8
Join($e, $u):  6 ©®™©®™ - is utf8