Question 38
Determine all functions $f: \mathbf{R} \to \mathbf{R}^+$ satisfying
$$
f(x + y) = f(x)f(y) (1 + (f(y) - 1)^{2009})
$$
for all $x, y \in \mathbf{R}$. (Here $\mathbf{R}^+$ is the set of all positive real numbers.)
$$
f(x + y) = f(x)f(y) (1 + (f(y) - 1)^{2009})
$$
for all $x, y \in \mathbf{R}$. (Here $\mathbf{R}^+$ is the set of all positive real numbers.)