Two young mathematicians think about the plots of functions.

Check out this dialogue between two calculus students (based on a true story):
Devyn
Riley, do you remember implicit differentiation?
Riley
Yes. We have an equation that defines a function, and ask about the derivative of that implicitly defined function.
Devyn
Exactly! If we have something like ...
Riley
This defines as a function of .
Devyn
But we could also use it to define as a function of !
Riley
Right!
Devyn
And we can find both and .
Riley
Absolutely. It’s almost the same work either way.
Devyn
How are and related to one another?
Riley
Hmm....
If we call and as the two functions defined by , how are and related?
There is no relationship. They are opposites. They are inverses. They are reciprocals.
What is the basic relationship between and ?
There is no relationship. They are opposites. They are inverses. They are reciprocals.