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October 23rd, 2018, 11:07 PM   #1
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A recurrence equation

Hello everybody,

Solve the recurrence equation $\displaystyle |f(x^2+1)-f(x^2-1)|=3x^2+2x+1$.

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October 24th, 2018, 06:58 AM   #2
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What do you mean by "recurrence equation"?
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October 24th, 2018, 02:04 PM   #3
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First be sure $\displaystyle f(x^2 +1) $ and $\displaystyle f(x^2 -1) $ is a polynomial function
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October 24th, 2018, 02:14 PM   #4
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Probably meant is a "recurrence relation" which is a type of equation defining a function through recursion. Explains why the polynomial is missing.
https://en.wikipedia.org/wiki/Recurrence_relation

Last edited by Arisktotle; October 24th, 2018 at 02:31 PM.
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October 24th, 2018, 10:39 PM   #5
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Quote:
Originally Posted by skipjack View Post
What do you mean by "recurrence equation"?
Hello,

Recurrence Equation -- from Wolfram MathWorld

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October 25th, 2018, 07:59 AM   #6
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Quote:
Originally Posted by idontknow View Post
First be sure $\displaystyle f(x^2 +1) $ and $\displaystyle f(x^2 -1) $ is a polynomial function
Why? As a trivial counter-example, what if $\displaystyle f(x^2 + 1) = x^2 - 1 + ln(x)$ and $\displaystyle f(x^2 - 1) = 3x + 5 + ln(x)$?

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October 25th, 2018, 09:34 PM   #7
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Quote:
Originally Posted by topsquark View Post
Why? As a trivial counter-example, what if $\displaystyle f(x^2 + 1) = x^2 - 1 + ln(x)$ and $\displaystyle f(x^2 - 1) = 3x + 5 + ln(x)$?

-Dan
Hello,

If $\displaystyle f(x^2 + 1) = x^2 - 1 + ln(x)$ and $\displaystyle f(x^2 - 1) = 3x + 5 + ln(x)$ , then what expression has $\displaystyle f(x)$?Thank you very much!

All the best,

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