Unique $f\left( x \right)$

Algebra Level 4

A real valued function satisfies the following conditions:

(1) $f \left( x-1 \right) +f \left( x+1 \right) = \sqrt{ 2 } f \left( x \right)$ for $x < -1$ or $x > 7$ .
(2) $f\left( x \right) =x \mbox{ for } 0\le x\le 7.$