like what the hell is this
#help me understand how domains and codomains work
vapid knoll
lapis furnaceBOT
winged sail
I think what you’ve got on that whiteboard is called a “composition of functions”.
To answer your original question, a domain is like a starting point for a function, and a codomain is like an ending point.
Your function is like a map (in mathematics literature functions are sometimes called maps) that start in the domain and takes you (ie finishes) in the codomain.
A composition of a function is basically when you apply a first function to a second function.
Let’s say you have $$ f \circ g$$.
What happened here is that you first apply your function g, which takes elements within the g domain and maps to the g codomain. Now you apply the function f to this g, in other words the domain of f is the same as the codomain of g (you start the f mapping where g finished if you will).
wanton agateBOT
Bottle03
winged sail
Sometimes people like to use the word input and output to describe the domain and codomain respectively. Ie the domain is where the input values are and the codomain is where the output values are.
What they’ve done on the white board is given you a specific example. In their example they have technically made a mistake which I will try to explain.
What they have written is:
$$f(x) = 20x + 15, g(x) = 5000f - 1000$$
The problem with this is that their function g is a function of x, but they wrote an f on the right hand side, what they should have said was
$$g(x) = 5000x -1000 \implies g(f(x)) = 5000f -1000$$
This means that when you put f(x) in the function g, you multiply the output of f by 5000 and then subtract 1000. And as they have done on the whiteboard, they have solved the problem in 2 ways (or Kasus)
wanton agateBOT
Bottle03
winged sail
In this case, x = 200, so f(x) = 4015. And when they do g(f(x)), in Kasus 1, they have done g(4015), which equals 20, 074, 000 (or 20.074.000).
I’m sorry I don’t speak Indonesian, but I hope that helps @vapid knoll
What I have described is an example of number 4 on that board, I believe that is “komposisi fungsi” or function composition
hybrid pond
basically, for $f:U\to V$, U is the domain and V is the codomain
wanton agateBOT
Robert
