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Math Help - Please help....

  1. #1
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    Please help....

    Can sumone pls show me how to do this question.
    Q.Suppose that f:N->N and g:N->N are defined by f(n)=n^3 and g(n)=n^2 for each natural number n.Show that g o f is not equal to f o g.
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  2. #2
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    Quote Originally Posted by dcapdogg
    Can sumone pls show me how to do this question.
    Q.Suppose that f:N->N and g:N->N are defined by f(n)=n^3 and g(n)=n^2 for each natural number n.Show that g o f is not equal to f o g.
    It can't be done, because they are equal:

    <br />
(f\circ g)(x)=f(g(x))=f(x^2)=(x^2)^3=x^6<br />

    <br />
(g\circ f)(x)=g(f(x))=g(x^3)=(x^3)^2=x^6<br />
.

    RonL
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  3. #3
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    oops i left a bit out

    g(n)=n^2-2
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  4. #4
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    Quote Originally Posted by dcapdogg
    g(n)=n^2-2
    In that case:

    <br />
(f\circ g)(x)=f(g(x))=f(x^2-1)=(x^2-2)^3 =x^6 - 6x^4 + 12x^2 - 8<br />

    <br />
(g\circ f)(x)=g(f(x))=g(x^3)=(x^3)^2-2=x^6-2<br />

    and so they are not the same function.

    RonL
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  5. #5
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    Quote Originally Posted by CaptainBlack
    In that case:

    <br />
(f\circ g)(x)=f(g(x))=f(x^2-1)=(x^2-2)^3 =x^6 - 6x^4 + 12x^2 - 8<br />

    <br />
(g\circ f)(x)=g(f(x))=g(x^3)=(x^3)^2-2=x^6-2<br />

    and so they are not the same function.

    RonL
    I find it fascinating that the last person that posted the same question left out the same detail.

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    User banned (7 days).
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