Something brought up in class.

1. Sep 16, 2004

JasonRox

I should have mentionned it, but I rather think about it first.

Suppose f:A->B and g:B->C

then g*f:A->C

That makes sense.

Is this possible? Think about it. If f has domain A, and g has range C, than how can f(x) equal anything, since the range of C is not equal to set A, which is what we need to calculate f.

f*g:B->?

I hope you understand.

2. Sep 16, 2004

fourier jr

no that definitely doesn't make sense. i think you're right, but you also shouldn't rock the boat. just do whatever it takes to get through the course.

3. Sep 16, 2004

Hurkyl

Staff Emeritus
That's not quite true; all we need is for x to be in A.

Although f*g certainly will not exist in general, can you come up with conditions for which it would?

edit: I'm assuming you're using the * symbol to mean composition

Last edited: Sep 16, 2004
4. Sep 16, 2004

mathwonk

well one needs to define upper star. for instance the usual definition of upper star is "precede by" so f*g would actually mean gof which is defined as above.

5. Sep 16, 2004

Hurkyl

Staff Emeritus
IMHO this is, in general, terrible advice. Asking questions is how you learn things (and sometimes can help other people learn things, because they were too shy to ask a question). The bar is so low that just "doing what it takes" will certainly harm your chances in future math classes in which you're expected to know this stuff learned in this class.

6. Sep 17, 2004

matt grime

There are two ways to write composition of functions, check which one your teacher uses. writing f*g to mean g composed with f is very common especially amongst logicians, who see it as more logical, and some applied people who read only read left to right.

7. Sep 17, 2004

Staff Emeritus
In algebra the composition leads to the concept of image and kernel. If f: A -> B, then f(a) is the image of A in B under f; the set of points in B that are images of points in A under the function f. And in algebra we have a zero element (group identity or whatever). Kernel f is the set of points in A that are mapped into the zero or identity element of B.

8. Sep 17, 2004

HallsofIvy

Staff Emeritus
I'm wondering if this wasn't supposed to be about the inverse functions.

If f:A->B and g:B->C then g*f:A->C.

If f and g are both invertible, then so is g*f and (g*f)-1= f-1*g-1:C->A.

9. Sep 17, 2004

JasonRox

I meant * as a composition.

I will ask to make sure.