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) \( f\left( x \right) =x \mbox{ for } 0\le x\le 7.\)