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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?
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December 2nd, 2016, 07:39 AM   #2
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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.)
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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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