0Answer:
Method 1:
Best approach: Let f(x-1) = 1 and f(x) = 1
So the sequence becomes : 1, 1, (√2) - 1, 1 - (√2), -1, -1, 1 - (√2), (√2) - 1, 1, 1, ...
i.e. f(x) is a periodic function with period 8 and after every four terms, terms start repeating with negative sign as shown above.
Method 2:
Let f(x)=a and f(x-1)=b then solve in terms of a and b we will get f(x+4)=-a so ans is -1
f(x+2) + f(x) = rt2 . f(x+1)...... i
f(x+3) + f(x+1) = rt2 . f(x+2) ............ii
f(x+4) + f(x+2) = rt2 . f(x+3)
Or f(x+4) + f(x+2) = 2f(x+2) - rt2 . f(x+1)....... from ii
So f(x+4) = f(x+2) - rt2. f(x+1)
So f(x+4) = - f(x)..from i
So answer = -1
