Question 5
Let $S$ be the set of real numbers greater than $-1$. Find all functions $f:S\to S$ such that
$$f(x+f(y)+xf(y))=y+f(x)+yf(x)$$
for all $x$ and $y$ in $S$, and $f(x)/x$ is strictly increasing for $-1\lt x\lt 0$ and for $0\lt x$.
$$f(x+f(y)+xf(y))=y+f(x)+yf(x)$$
for all $x$ and $y$ in $S$, and $f(x)/x$ is strictly increasing for $-1\lt x\lt 0$ and for $0\lt x$.