Inverses exist as part of a Group, which need a set of elements and an operation. Given a set of functions, and the operation of composition, inverses must be functions. And what about Closure? The inverse of a function must be a function. The inverse of a relation could be a relation, but f(x) means a function of x. Why do they insist on making their own version of mathematics? Aren't there any real mathematicians on the committee?