# Thread: Need help finding formulas for f o g and g o f?

1. ## Need help finding formulas for f o g and g o f?

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?

2. As far as I know, you've already found them.

3. composition of mappings $\displaystyle f :X \to Y$ and $\displaystyle g:Y \to Z$ is mapping $\displaystyle h=f°g:X \to Z$ defined by:

$\displaystyle (f°g)(x)=g(f(x))$

so i think should be :

$\displaystyle f°g=x(x-2)$

$\displaystyle g°f=x^2-2$

4. Originally Posted by yeKciM
composition of mappings $\displaystyle f :X \to Y$ and $\displaystyle g:Y \to Z$ is mapping $\displaystyle h=f°g:X \to Z$ defined by:

$\displaystyle (f°g)(x)=g(f(x))$

so i think should be :

$\displaystyle f°g=x(x-2)$

$\displaystyle g°f=x^2-2$
No, $\displaystyle (f\,\circ\,g)(x)=\mathbf{f(g(x))}$. So the OP has it right.

5. Ohh haha i thought the question would be harder. Thanks

6. Originally Posted by eumyang
No, $\displaystyle (f\,\circ\,g)(x)=\mathbf{f(g(x))}$. So the OP has it right.
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 $\displaystyle x \in X ) : h(x)=g(f(x))$

7. 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
You are probably wrong somewhere because indeed, composite functions are defined as $\displaystyle (f \circ g)(x) = f(g(x))$.

8. Originally Posted by Bacterius
You are probably wrong somewhere because indeed, composite functions are defined as $\displaystyle (f \circ g)(x) = f(g(x))$.

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 $\displaystyle x \in X$ associates one and onley one element $\displaystyle y \in Y$. That's definition of mapping...

Let we say that X,Y,Z were not empty piles and that we have functions $\displaystyle f : X \to Y$ and $\displaystyle g: Y \to Z$. Now meaning that f will map X to Y (and f is function of X) $\displaystyle y = f(x)$ and g now will map Y to Z (and g is function of y) meaning $\displaystyle g(y) =g(f(x))$
so when u have $\displaystyle (f \circ g)(x) = g(f(x))$

and that way u'll have maping $\displaystyle h=(f \circ g) : X \to Z$
defined for every $\displaystyle x \in X$

where do u think i'm wrong ?
P.S. sorry if I'm boring with this but I'm confused

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# find the formula for the compostion of gof

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