Solving Math Blog Problem - Gaussianos.com

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The discussion revolves around a mathematical problem from Gaussianos.com, where the goal is to find a function ƒ(t) that satisfies a specific equation involving variables x and y. The initial poster, an engineering student, is unsure whether the task requires a general function or a particular solution. Participants suggest starting with simple functions, noting that ƒ(t) = t is a straightforward solution. However, there is a desire to explore more analytical approaches to uncover a broader range of solutions. The conversation emphasizes the challenge of solving the equation and the interest in deeper mathematical exploration.
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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!
 
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Anymodal said:
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.
 
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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!
 
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