- #1

LCSphysicist

2020 Award

- 393

- 80

## Homework Statement:

- "Find all functions f: R in R such that x and y belong to R" (R is obviously real space) (continuation in the blank frame

## Relevant Equations:

- \n

$$f(xf(y) + f(x)) + f(y^2) = f(x) + yf(x + y)$$

A tricky question, i think.

First fact i found was:

f(f(0)) = 0

So i separate it in two types of functions

f(0) = 0 and f(0) = u.

I was trying to analyzing both cases, with the cases where x = y and x = -y but is is rather extended way, so i believe there is a better attempt to solve the question

Anyway i am not sure if we have a solution with explicit functions (f(x) = x²) or if the answer end to be something like (f(x) + f(y) + ...)

Any tips?

@fresh_42

A tricky question, i think.

First fact i found was:

f(f(0)) = 0

So i separate it in two types of functions

f(0) = 0 and f(0) = u.

I was trying to analyzing both cases, with the cases where x = y and x = -y but is is rather extended way, so i believe there is a better attempt to solve the question

Anyway i am not sure if we have a solution with explicit functions (f(x) = x²) or if the answer end to be something like (f(x) + f(y) + ...)

Any tips?

@fresh_42