Write a Python function inverse$($A$,$ B$,$ f$)$ that returns a list of lists describing the inverse of the function f : A $$ B$.$ The ordered pairs in the inverse should be sorted in ascending order of each pair$$s first element. If the argument f is not a function from A to B$,$ or if no well$-$defined inverse exists $($i$.$e$.,$ the inverse is not itself a function$),$ return None.

For example, calling inverse$($A$,$ B$,$ f$)$ with the above variable values should return None. But if you were to define your variables like this: