What does "unique" mean? I ran into a trivial exercise. If a function f is bijective, show that it has an inverse. That's easy. But then, the question goes: if f has an inverse, show that it is unique. I'm not really sure what is meant by "unique." I would assume it is has to do with the function's one-to-one correspondence. That each element in the function is taken cared of (mapped) one at a time. Is this a good analogy? This is not homework by the way.