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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. |
