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. :confused:

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- Aug 17th 2006, 02:33 AMdcapdoggPlease 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. :confused: - Aug 17th 2006, 02:40 AMCaptainBlackQuote:

Originally Posted by**dcapdogg**

$\displaystyle

(f\circ g)(x)=f(g(x))=f(x^2)=(x^2)^3=x^6

$

$\displaystyle

(g\circ f)(x)=g(f(x))=g(x^3)=(x^3)^2=x^6

$.

RonL - Aug 17th 2006, 02:44 AMdcapdoggoops i left a bit out
g(n)=n^2-2

- Aug 17th 2006, 03:23 AMCaptainBlackQuote:

Originally Posted by**dcapdogg**

$\displaystyle

(f\circ g)(x)=f(g(x))=f(x^2-1)=(x^2-2)^3$$\displaystyle =x^6 - 6x^4 + 12x^2 - 8

$

$\displaystyle

(g\circ f)(x)=g(f(x))=g(x^3)=(x^3)^2-2=x^6-2

$

and so they are not the same function.

RonL - Aug 17th 2006, 04:04 AMtopsquarkQuote:

Originally Posted by**CaptainBlack**

-Dan - Aug 17th 2006, 04:38 AMThePerfectHacker
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