[jameshart]

That it has an inverse.

If f(a) = f(b) for a≠b then f can't have an inverse.

Suppose f has inverse g; then g(f(x)) must = x for all x.

But then g(f(a)) would have to equal a, and g(f(b)) would have to equal b. But they can't, because f(a)=f(b)