It could be the cycle of Xanth, by Piers Anthony. First tome is A Spell for Chameleon, published in 1977 .
Xanth is a magical world where every inhabitant has power. Like all natural elements such as plants. This country is also populated by magic animals (mandrakes, unicorns, harpies, ...) which are the result of crossings of vulgar species (beings without magical powers). Some powers are very useful (metamorphosis), other are very useless (changing hair colour, or creating pink spots). Your power can defines your career.
If at the age of 25, a resident of Xanth did not discover his power, he was banished from Xanth and sentenced to exile in Mundania .
We follow the story of Bink, a young man without any apparent power ...
We find out later that his talent is in fact immunity to magical harm, which is really powerful in a world where quite everything is magic !
It's a very funny universe with many worldplays and comic situations.
I don't remember any dragon, but there's for sure a manticore, as you can see