Something brought up in class.

[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.

Then they talked about f*g!

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.

 

[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.

 

[Hurkyl]

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.

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

 

[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.

 

[Hurkyl]

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.

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.

 

[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.

 

[selfAdjoint]

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.

 

[HallsofIvy]

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.

 

[JasonRox]

I meant * as a composition.

I will ask to make sure.