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

  1. #1
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    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?
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  2. #2
    A Plied Mathematician
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    As far as I know, you've already found them.
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  3. #3
    Senior Member yeKciM's Avatar
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    composition of mappings $\displaystyle f :X \to Y$ and $\displaystyle g:Y \to Z$ is mapping $\displaystyle h=fg:X \to Z$ defined by:

    $\displaystyle (fg)(x)=g(f(x))$


    so i think should be :

    $\displaystyle fg=x(x-2)$

    $\displaystyle gf=x^2-2$
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  4. #4
    Senior Member eumyang's Avatar
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    Quote Originally Posted by yeKciM View Post
    composition of mappings $\displaystyle f :X \to Y$ and $\displaystyle g:Y \to Z$ is mapping $\displaystyle h=fg:X \to Z$ defined by:

    $\displaystyle (fg)(x)=g(f(x))$


    so i think should be :

    $\displaystyle fg=x(x-2)$

    $\displaystyle gf=x^2-2$
    No, $\displaystyle (f\,\circ\,g)(x)=\mathbf{f(g(x))}$. So the OP has it right.
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  5. #5
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    Ohh haha i thought the question would be harder. Thanks
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  6. #6
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by eumyang View Post
    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 $\displaystyle x \in X ) : h(x)=g(f(x))$
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  7. #7
    Super Member Bacterius's Avatar
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    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 $\displaystyle (f \circ g)(x) = f(g(x))$.
    Last edited by mr fantastic; Jul 21st 2010 at 02:34 AM.
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  8. #8
    Senior Member yeKciM's Avatar
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    Quote Originally Posted by Bacterius View Post
    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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