The function recaptcha_get_html() has to be visible from the file you're trying to use it : to be able to call that function, PHP must know it.
Here, you are using this function in register.php.
But that function is (I guess) defined in another file.
Which means you have to include or require that other file, from register.php (or another file that's required by it).
See the require and include, and their *_once* versions : require_once and include_once.
For example, at the beginning of register.php, you could have something like this :
require_once dirname(__FILE__) . '/../libraries/recaptcha.php';
Of course, up to you to adapt the path to the file ;-)