FunctionHard
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
Create a free account to view solution
View Solution FreeMore Function Questions
If f(x) = cos x + sin x, where [.] denotes the greatest integer function, then which of the following is not correct...The value of b and c for which the identity f ( x + 1) - f (x) = 8x + 3 is satisfied, where f(x) = bx2 + cx + d, are -...Function f(x) = sin log has domain...If f : R+ → R+, f(x) = x2 + 1/x2 and g : R+ → R+, g(x) = ex then (gof) (x) equals-...If f (x) = , then =...