Question 183
Let $b$ be a positive real number. Find all functions $f: \mathbb{R} \to \mathbb{R}$ satisfying
$$
f(x+y) = f(x) \cdot 3^{b^y+f(y)-1} + b^x\left(3^{b^y+f(y)-1} - b^y\right) \quad \forall x, y \in \mathbb{R}.
$$
$$
f(x+y) = f(x) \cdot 3^{b^y+f(y)-1} + b^x\left(3^{b^y+f(y)-1} - b^y\right) \quad \forall x, y \in \mathbb{R}.
$$