Find g ° f
f(x) = {(1, 2), (2,1), (3,1), (4, 4)}
g(x) = {(1, 2), (2,4), (3, 1), (4, 3)}
Can you check if there is a typo?
As it is, f(x) is not onto, i.e. f(2)=f(3)=1.
To find g°f, complete the following table:
x u=f(x) g(u) = g ° f(x)
1 2 4 = g°f(x)
2 1 2
3 1 2
4 4 3
Therefore
g°f : {(1,4),(2,2) ....}
As supplementary information, read up
http://en.wikipedia.org/wiki/Function_composition
Well, I am suppose to find the composition of functions from a figure. If you don't mind I uploaded a photo of it on photobucket. Can you take a look, and offer any suggestions for the first problem, so that I can get an idea? Since this forum will not let me post a link I can give directions on how to find the photo. First, go to search bar and type: flutegirl516. Then, this message will appear: Are you looking for the Photobucket user flutegirl516? Click on this. Then you will see the photo album. There is only one picture.
Also, click "View as slide show" to make it larger. Tell me if you can view it okay. Thanks for any helpful replies :)
I read the the link you provided previous to posting this discussion, but I was still confused.
Sorry, I am not able to find the link according to your directions, probably we have different search bars.
You can try posting the link that following the prefix
http://media.photobucket.com/
and I can append it myself.
I'm using the search bar at the very top right-hand corner, then I enter: flutegirl516. It will say no matches found, but it will say: Are you looking for the Photobucket user flutegirl516?
You can also try using the search bar drop down menu and clicking on "Users," and then enter flutegirl516. The album should pop up. Try it, hopefully you will be able to view it.
Yes, indeed, I found it when I used Photobucket's search bar instead of the browser's search bar.
For reference, here's the link:
http://s1193.photobucket.com/albums/aa348/flutegirl516/?action=view¤t=Screenshot2011-02-15at61144PM.png
You have correctly represented the two functions, so there is no typo.
In case it is not clear how composition works, you only have to imagine that the range of f(x), i.e. the right part of f(x), is merged with the domain of g(x), or the left part of g(x).
You can then follow the arrows from the domain of f(x) to the codomain of g(x). For example, f(1)=2, g(2)=4, which is exactly what is in the table I posted earlier, namely
g°f=g(f(x))=g(f(1))=g(2)=4
It is easier than you can imagine!
ooOo I think I get it now. . .
Great!
Ok so
g ° f = {(1, 4), (2, 2), (3, 2), (4,3)}
There are two 1s in the range of f(x) though (1,2) and (3,1). . .Does that mean anything?
Is this correct:
Does g ° h = {(1, 2), (2?, 2?), (3, 2), (4, 1)}? For this one there was no 2 in the range of h.
Also, for h^2 = h ° h, what am I suppose to square? Domain (x) or Range (y).