As far as I know, you've already found them.
I stumbled upon this question in my text book :
Let f and g be polynomials defined by f(x)=x-1 and g(x)=x^2 -1.
Find formulas for f o g and g o f.
I dont fully understand what they mean by finding a formula.
so we no fog = (x^2-1)-1 = x^2-2
and gof =(x-1)^2 -1= x^2-2x
Soo how exactaly do we find a formula?
hmmm... sorry but now i'm confused. First I thought that i forgot definition of composition of mappings, so I double check it in few books I jused to learn from... And I didn't forgot it. Maybe my books are wrong ? I doubt that because authors are OK... not some "funny" people. Hehehehe
i forgot one line... but it's the same after defined by :
(for every
You are probably wrong somewhere because indeed, composite functions are defined as .hmmm... sorry but now i'm confused. First I thought that i forgot definition of composition of mappings, so I double check it in few books I jused to learn from... And I didn't forgot it. Maybe my books are wrong ? I doubt that because authors are OK... not some "funny" people. Hehehehe
let's look at it this way...
By mapping (or function ) f , pile X to pile Y we imply every method (algorithm or procedure or . . . ) by the which for every element associates one and onley one element . That's definition of mapping...
Let we say that X,Y,Z were not empty piles and that we have functions and . Now meaning that f will map X to Y (and f is function of X) and g now will map Y to Z (and g is function of y) meaning
so when u have
and that way u'll have maping
defined for every
where do u think i'm wrong ?
P.S. sorry if I'm boring with this but I'm confused