Let g(x) be a function such that g(x+1) + g(x-1)=g(x) for every real x.Then for what value of p is the relatio

Question

Let g(x) be a function such that g(x+1) + g(x-1)=g(x) for every real x.Then for what value of p is the relation g(x+p)=g(x) necessarily true for every real x?
(a) 5
(b) 3
(c) 2
(d) 6

Answer 1

I am unable to construct such a function except for the trivial g(x) = 0 for all x. For this function, any p would do.

Answer 2

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Answer 3

frankly i feel it will be true for p=0 alone

Answer 4

Answer is d.