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December 2nd, 2016, 07:05 AM   #1
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Polynomial function transform two function

Hello,
I have polynomial function (Blue function) and write this to two independent function.

Now red function is F(x) based F0(x) and F1(x).
How can write red function?
Thanks
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 fx.JPG (44.5 KB, 7 views) ffx.JPG (22.5 KB, 6 views)

 December 2nd, 2016, 07:39 AM #2 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Is that first thing written in f(x) a 4? That is, is $\displaystyle f(x)= 4+ 3x+ 5x^2+ 7x^3+ 2x^4+ 5x^5$? Which you then separate into "even" and "odd" powers $\displaystyle = (4+ 5x^2+ 2x^4)+ (3x+ 7x^3+ 5x^5)$ and factor "x" out of the odd powers $\displaystyle = (4+ 5x^2+ 2x^4)+ x(3+ 7x^2+ 5x^4)$ You then also have defined $\displaystyle f_0(x)= 4+ 5x^2+ 2x^4$ and $\displaystyle f_1(x)= 3+ 7x^2+ 5x^4$. Then, yes, the function above is $\displaystyle f(x)= f_0(x)+ xf_1(x)$ (It is not a good idea to use "x" as a variable and also as a multiplication sign which you appear to have done! Use "*" if not just "juxtaposition" to indicate multiplication.) Thanks from topsquark and life24
December 2nd, 2016, 08:29 AM   #3
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Exactly but we have power 2
I problem with this.
I rewrite the red function.
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Last edited by life24; December 2nd, 2016 at 08:32 AM.

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