Re: Types of functions and relations

Michael Stemper wrote: 
However, you include polynomial functions, even going to the extent of
viewing them differently by degree:

	Right. I wrote it hastily.


Composite. 


Any function can trivially be written as the composite of two functions,
so that's a pretty broad category.

It was the more the concept that I was after. A composite function is a very precise idea about functions that I thought should be made explicit. It's not quite what I was after, like positive or negative, but isn't entirely uninteresting either.




Inverse. 


Of the two functions
f(x)=2y
g(y)=x/2
which is the "inverse" function? Do you possibly mean "invertible"?

I meant inverse. Not all functions has inverses, just bijective ones, and there are also left and right inverses. Using the term "inverse function" one needs to specify another function that it is relative to or have it known from the context. Like, Suppose f(x) = x. Then g(x) = 1/x is the inverse of f.




Monotonic.
Injective.



I believe that, given suitable restrictions of domain and range, any
monotonic or injective function is invertible, and vice-versa.

If you restrict domain and range too much in the extreme then the functions will not be very interesting and you can pretty much have whatever of those properties you wish.




Given your examples, I'm guesing that you're only interested in functions
that map from one subset of the reals to another. Is this correct? Are
you not interested in functions of:
- more than one variable
- non-real variables
- non-real (ordered n-tuples, complex numbers, vectors, matrices) outputs

My experience with functions is pretty much limited to some basic set theory and functions used in real analysis. I'd be open to learn of other types of functions, but I could not list any myself. I've recently been learning about vector spaces of continuous functions and so have been exposed to functions whose domains are functions, which was really elegant in an abstract sort of way.


	Thanks for the help, Adam.
.