If f : R → R is a function satisfying the property $f (x +1)+ f (x + 3) = 2, ∀\, x∈R$, then the period of f (x) is

3 4 7 none of these

4

$f (x +1)+ f (x + 3) = 2, f (x + 3)+ f (x + 5) = 2$ $f (x +1)− f (x + 5) = 0 ⇒ f (x +1) = f (x +5) ⇒ f (x) = f (x + 4)$ Hence period is 4.