- #1
LCSphysicist
- 644
- 161
- 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