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• onchange="check_extension(one)"

Here one is the Node with the id "one", one is not the string "one"

• document.getElementById("$field_id");

Even if $field_id is the id "one", "$field_id" is a different string
So getElementById("$field_id") will give you the node with id "$field_id", not the node with id "one".

Fixes

onchange="check_extension('one')"

and

document.getElementById($field_id)

Also I discourage naming string variables with a leading $

• onchange="check_extension(one)"

  Here one is the Node with the id "one", one is not the string "one"

• document.getElementById("$field_id");

  Even if $field_id is the id "one", "$field_id" is a different string
  So getElementById("$field_id") will give you the node with id "$field_id", not the node with id "one".

Fixes

onchange="check_extension('one')"

and

document.getElementById($field_id)

Also I discourage naming string variables with a leading $