Question 5
Determine all functions $f:\mathbb R\to\mathbb R$ satisfying:
1. There is a real number $M$ such that $f(x)\lt M$ for every real $x$.
2. For all real $x,y$,
$$f(xf(y))+yf(x)=xf(y)+f(xy).$$
1. There is a real number $M$ such that $f(x)\lt M$ for every real $x$.
2. For all real $x,y$,
$$f(xf(y))+yf(x)=xf(y)+f(xy).$$