In  AlphaUserPoint, recaptcha is using to fight spam on your site. But first you must have a key from www.recaptcha.com. This key must you have. Recaptcha is using in the invite plugin. You can insert a link to this page: 

Go to the backend, login and select  "Menu" and  click one menu.

Click on "New"  and then click on AUP. Click on Invite. 

You go to the link editing page. At the right side you can see de link options: 

Then you see on the right Parameters(Basic) and there you can add your reCAPTCHA API key...