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Functional Equations

Anonymous Sun 12 Apr 15:46:39 2020 No.11557695 View Reply Original Report

Quoted By: >>11557708 >>11558128

I am a brainlet , on Functional Equations .
I need to learn how these things . Where do I start with the most basic Functional Equations ? Any book ?

Anonymous

Anonymous Sun 12 Apr 2020 15:49:56 No.11557708 Report

Quoted By: >>11557710 >>11557743 >>11557768

>>11557695
There's no general rule, so you actually have to be somewhat smart. Often it is a good idea to substitute something into the function that will give you similar terms, e.g. in your pic, sub in 1/x.

Anonymous

Anonymous Sun 12 Apr 2020 15:50:57 No.11557710 Report

Quoted By: >>11557768

>>11557708
>There's no general rule, so you actually have to be somewhat smart
Incidentally, this is why it's rarely ever seen in schools.

Anonymous

Anonymous Sun 12 Apr 2020 15:57:47 No.11557740 Report

Quoted By:

f(x) + 2 f(1/x) = 2x
>Replace x with 1/x
f(1/x) + 2 f(x) = 2/x
2f(1/x) + 4 f(x) = 4/x
>Subtract the original equation
3 f(x) = 4/x - 2x
f(x) = 4/(3x) - 2/3x

Anonymous

Anonymous Sun 12 Apr 2020 15:58:51 No.11557743 Report

Quoted By: >>11557766

>>11557708
I understand that practice is the key to getting good at these . Any sources of practice that slowly builds up from easy to hard ?

Anonymous

Anonymous Sun 12 Apr 2020 16:04:57 No.11557766 Report

Quoted By:

>>11557743
idk, make up some functional equations and see if you can solve them.

Anonymous

Anonymous Sun 12 Apr 2020 16:06:03 No.11557768 Report

Quoted By: >>11557777

>>11557708
>>11557710
Yet integration is core in schools. Maybe it's just not that important.

Anonymous

Anonymous Sun 12 Apr 2020 16:09:32 No.11557777 Report

Quoted By:

>>11557768
>Implying the integration done in schools isn't literally "remember this method and remember when to apply it".
Even in a lot of universities nowadays, they don't require you to figure out any difficult integrals.

Anonymous

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Anonymous Sun 12 Apr 2020 17:31:17 No.11558128 Report

Quoted By:

>>11557695
This is the reason why I pound your mom at night, she's a Q(t)

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