Re: Types of functions and relations

In article <1ISdnaNxOs2spu3fRVn-qg@xxxxxxxxxx>, aboom writes:

>I seek to understand types of functions and the relation properties that
>they obey, if there is any at all.
>
>Please add to the list below other types of functions. It seems that
>designating a "type" of function means that such functions have
>interesting properties, such as integrals over even and odd functions.
>Note, I do not include specific groups of functions such as trigometric,
>exponential, etc, because I seek properties that any function might have.

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

>Degrees: linear, quadratic, cubic,etc.

>Composite.

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

>Inverse.

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

>Monotonic.
>Injective.

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

>Bijective.

Any bijective function is invertible.

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

>What is the name of the set whose elements constitute the pairs that the
>function maps to. for instance, let f: A -> B be a function with
>elements of the set F <= AxB. What is the formal name of F?

"The function f."

--
Michael F. Stemper
#include <Standard_Disclaimer>
Build a man a fire, and you warm him for a day. Set him on fire,
and you warm him for a lifetime.

.

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