VN-TST 1994 Problem 5

Determine all functions $f: \mathbb{R} \mapsto \mathbb{R}$ satisfying

$$f\left(\sqrt{2} \cdot x\right) + f\left(4 + 3 \cdot \sqrt{2} \cdot x \right) = 2 \cdot f\left(\left(2 + \sqrt{2}\right) \cdot x\right)$$

for all $x$ .