Roger, if you run your code with -w, it gives you warning:

"my" variable $k masks earlier declaration in same scope at a.pl line 
+6.
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Once you resolve the warning by only declaring $k once, everything is now fine:

use strict;

my $k = 1;
print "wanted: \$k = $k, got " . InvestigateValue() . "\n";

$k = 2;#modified
print "wanted: \$k = $k, got " . InvestigateValue() . "\n";

sub InvestigateValue
{
    return defined $k ? $k : 'undef';
}
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