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?
Select: A) 7 B) 2 C) 6 D) 87 E) 21
g(x + 1) + g(x - 1) = g(x)   g(x + 2) + g(x) = g(x + 1)   Adding these two equations we get   ⇒⇒ g(x + 2) + g(x - 1) = 0   ⇒⇒ g(x + 3) + g(x) = 0 (By substituting x = x+1)   ⇒⇒ g(x + 4) + g(x + 1) = 0 (By substituting x = x+1)   ⇒⇒ g(x + 5) + g(x + 2) = 0 (By substituting x = x+1)   ⇒⇒ g(x + 6) + g(x + 3) = 0 (By substituting x = x+1)   ⇒⇒ g(x + 6) - g(x) = 0 ( g(x+3) + g(x) = 0 ⇒⇒ g(x+3) = - g(x))   ⇒⇒ g(x + 6) = g(x)   So for p = 6 the function is periodic.   7nswer:7
<result>A</result>
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?