FunctionMedium
Question
If f : R → R is a function satisfying the property f(x + 1) + f(x + 3) = K ∀ × ∈ R then the period of f (x) is -
Options
A.4
B.K
C.1
D.π
Solution
f (x + 1) + f (x + 3) = K ∀ x
put x = -1
f (0) + f (2) = K .........(i)
put x = 1 f (2) + f (4) = R .......(ii)
from (i) & (ii)
f (4) = f (0) = 0 ⇒ period = 4
put x = -1
f (0) + f (2) = K .........(i)
put x = 1 f (2) + f (4) = R .......(ii)
from (i) & (ii)
f (4) = f (0) = 0 ⇒ period = 4
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