please solve this one!!

let f(x) be a function such that f(x-1) +f(x+1)= √2f(x)
then find the period of f(x).

5 Answers

is d period 8??

HINT : .... get rid of root(2) and keep solving .......

subs x as x+1
so
f(x)+f(x+2)=âˆš2f(x+1)
subs x as x-1 in d orig eqn
f(x-2)+f(x)=âˆš2f(x-1)

add both
f(x-2)+f(x+2)+2f(x)=âˆš2(f(x-1)+f(x+1))
f(x-2)+f(x+2)+2f(x)=2f(x)
f(x-2)+f(x+2)=0

subx x as x+2
f(x)+f(x+4)=0

subs x as x-2
f(x-4)+f(x)=0
subtract...both
f(x+4)=f(x-4)

subs x as x-4
f(x)=f(x-8)

so d period is 8

okay i got it.. i don't know the answer but it is in the options so i think it's correct

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