Question 128
Prove that the functional equations
$$
\begin{aligned}
f(x+y) &= f(x) + f(y) \\
\text{and}\quad f(x+y+xy) &= f(x) + f(y) + f(xy) \quad (x, y \in \mathbb{R})
\end{aligned}
$$
are equivalent.
$$
\begin{aligned}
f(x+y) &= f(x) + f(y) \\
\text{and}\quad f(x+y+xy) &= f(x) + f(y) + f(xy) \quad (x, y \in \mathbb{R})
\end{aligned}
$$
are equivalent.