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Q
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...
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
E
4
A
5
B
3
C
2
D
6
E
4
Solution
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) =...
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
⇒ g(x + 4) + g(x + 1) = 0
⇒ g(x + 5) + g(x + 2) = 0
⇒ g(x + 6) + g(x + 3) = 0
⇒ g(x + 6) – g(x) = 0
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