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.

As follows:

I would like to know how these are done though.

Can anyone show me?

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.

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!

Thanks Alan. :)

Thank you so much Alan!

https://web2.0calc.com/questions/help_95995