Solving Math Blog Problem - Gaussianos.com

[Anymodal]

Hi, I came upon this problem in an old paper in my desk. I remember that I read it on the internet (I'm almost sure from the math blog gaussianos.com) and couldn't solve it. I study engineering.
The problem is to find an ƒ(t) such that:

ƒ[(x^2) + x*y + ƒ(y)] = [ƒ(x)]^2 + x*ƒ(y) + y

I'm not sure if it asked to find a general function that meets this condition or just a particular solution.
Anyone knows how to get their hands around it?
Thanks!

 

[PeroK]

Hi, I came upon this problem in an old paper in my desk. I remember that I read it on the internet (I'm almost sure from the math blog gaussianos.com) and couldn't solve it. I study engineering.
The problem is to find an ƒ(t) such that:

ƒ[(x^2) + x*y + ƒ(y)] = [ƒ(x)]^2 + x*ƒ(y) + y

I'm not sure if it asked to find a general function that meets this condition or just a particular solution.
Anyone knows how to get their hands around it?
Thanks!

You could always try a few functions, starting with the simplest you can think of.

 

[Anymodal]

You're right. f (t)=t is the simplest solution... how could have I not seen it... anyway I am still curious about how to approach this problem to solve it analytically to find the more general and widest solution possible.

Thank you very much!