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Find all functions $$f:\mathbb R \to \mathbb R$$ that satisfy $$f(x) + f \left( \frac{x - 1}{x} \right) = \frac{5x^2 - x - 5}{x}$$ for all nonzero x.

May 30, 2020
edited by littlemixfan  May 30, 2020

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As follows:

May 31, 2020

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I would like to know how these are done though.

Can anyone show me?

May 31, 2020
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As follows:

Alan May 31, 2020
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Thanks Alan,

I had no idea how to do these and it did not occur to me to just try linear.

It does say find all functions.  Are you sure you have found all of them?

I need to ponder on your answer.

Melody  Jun 1, 2020
edited by Melody  Jun 1, 2020
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Hi Melody,  I'm not 100% sure I've got all of them.  However, there can't be any higher polynomials as any extra multiplying coefficients would turn out to be zero. I certainly can't think of any other forms that would fit!

Alan  Jun 1, 2020
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Thanks Alan.  :)

Melody  Jun 1, 2020
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Thank you so much Alan!

littlemixfan  Jun 6, 2020
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https://web2.0calc.com/questions/help_95995

Jun 1, 2020