Unique f(x)f\left( x \right)

Algebra Level 4

A real valued function satisfies the following conditions:

(1) f(x1)+f(x+1)=2f(x) f \left( x-1 \right) +f \left( x+1 \right) = \sqrt{ 2 } f \left( x \right) for x<1 x < -1 or x>7 x > 7 .
(2) f(x)=x for 0x7. f\left( x \right) =x \mbox{ for } 0\le x\le 7.

Find the value of f(87)f(87).

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