Find all functions of with the property
Does this help in any way? I was thinking that somehow I could get the to cancel out but I couldn't get it to work.
The RHS can be multiplied by to give:
but I don't think that's helping.
It's an interesting question. I hope someone here can solve it!
EDIT: Perhaps you could try case analysis. When x=0:
[tex]f(f(y))=(f(0))^2+y[/tex]
f(0) has an unknown value so it might not help. However, we have successfully eliminated a term which is beneficial!