A function `f` is have inverse it should be a bijection

A condition for a function y=f(x) to have an inverse is that it should be

The inverse of a bijection is unique

The inverse of a bijection is also a bijection

Is the reciprocal function a bijection ?

Let the function f:A rarr B have an inverse function f^(-1): B rarr A , then the nature of the function f is __