I found and saw your diagram
If I recall correctly
F°h°G is read as F "follows" h "follows" G
so G would be done first, then h, etc
G: A --> C
h: C --> B
F: B --> C
so you have A -->C
I don't know if this helped, have not done this stuff in 40 years.
So, I uploaded the figure in photobucket, and if you type flutegirl516 in the search bar you will see it's the first photo.
F:B→C, h:C→B, and G:A→C
Is F°h°G defined? If so, what is its domain and range?
Yes it is defined. And I thought that the domain and range of F ° h ° G = A -> B. But i don't think this is correct. Why would this be considered defined? I'm desperate to understand.
8 answers
Thank you for replying. So if this question makes any sense: How do you know I must start with G first? It makes sense because it actually works when I create samples, but it seems that I am working backwards, why is that? But I think I am kind of following. . .
As I recall the same notation is used in the function notation.
in the notation
f°h , it means that f follows h
e.g. in "eating follows cooking", which do you do first?
most textbooks define
f°h to mean f(h(x))
Since in f(h(x)) you work on the Hh(x) first and there is no confusion, I always have preferred the
f(h(x)) notation.
in the notation
f°h , it means that f follows h
e.g. in "eating follows cooking", which do you do first?
most textbooks define
f°h to mean f(h(x))
Since in f(h(x)) you work on the Hh(x) first and there is no confusion, I always have preferred the
f(h(x)) notation.
So, how would F ° h ° G be defined? It seems the domain is A and the range is C, right? But why does it exist? Does it exist because it can be proven using sample problems or it it because of the figure and the direction of the arrows? IDK. That's what I am having trouble understanding.
Sorry to join in the discussion.
It all comes to the basic definition:
g°f is read as "g of f", just like g(x) is read as g of x, or f(x) is f of x or function of x.
so g°f=(g*deg;f)(x)=g(f(x)) which explains why f(x) has to be evaluated first before g.
If you say F°h°G as F of h of G, then it automatically comes to mind as: F(h(G(x))), in which case it is obvious that G should be evaluated first.
Yes, you have to follow the arrows, because for example, in h°G, the range of G is fed into the domain of h. So h°G exists IF AND ONLY IF the range of G matches the domain of h, which is the case here.
Since the same applies to F°h, therefore F°h°G exists, assuming F,h,and G are functions, therefore they are one-to-one.
It all comes to the basic definition:
g°f is read as "g of f", just like g(x) is read as g of x, or f(x) is f of x or function of x.
so g°f=(g*deg;f)(x)=g(f(x)) which explains why f(x) has to be evaluated first before g.
If you say F°h°G as F of h of G, then it automatically comes to mind as: F(h(G(x))), in which case it is obvious that G should be evaluated first.
Yes, you have to follow the arrows, because for example, in h°G, the range of G is fed into the domain of h. So h°G exists IF AND ONLY IF the range of G matches the domain of h, which is the case here.
Since the same applies to F°h, therefore F°h°G exists, assuming F,h,and G are functions, therefore they are one-to-one.
Sorry to join in the discussion.
It all comes to the basic definition:
g°f is read as "g of f", just like g(x) is read as g of x, or f(x) is f of x or function of x.
so g°f=(g°f)(x)=g(f(x)) which explains why f(x) has to be evaluated first before g.
If you say F°h°G as F of h of G, then it automatically comes to mind as: F(h(G(x))), in which case it is obvious that G should be evaluated first.
Yes, you have to follow the arrows, because for example, in h°G, the range of G is fed into the domain of h. So h°G exists IF AND ONLY IF the range of G matches the domain of h, which is the case here.
Since the same applies to F°h, therefore F°h°G exists, assuming F,h,and G are functions, therefore they are one-to-one.
It all comes to the basic definition:
g°f is read as "g of f", just like g(x) is read as g of x, or f(x) is f of x or function of x.
so g°f=(g°f)(x)=g(f(x)) which explains why f(x) has to be evaluated first before g.
If you say F°h°G as F of h of G, then it automatically comes to mind as: F(h(G(x))), in which case it is obvious that G should be evaluated first.
Yes, you have to follow the arrows, because for example, in h°G, the range of G is fed into the domain of h. So h°G exists IF AND ONLY IF the range of G matches the domain of h, which is the case here.
Since the same applies to F°h, therefore F°h°G exists, assuming F,h,and G are functions, therefore they are one-to-one.
Sorry for the double post. Skip the first one, which contains a typo on the fourth line.
Okay thank you for the clarification :)
1 answer