There is
no relationship. They are opposites. They are inverses. They are reciprocals.
Two young mathematicians think about the plots of functions.
- 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?