Question

Let a function satisfying f(x + 4) + f (x - 4) = f (x) for all
real x is periodic, then period T for them is
A. 8
B. 12
C. 16
D. 24​

Answer 1

Answer:

8 is answer of this question

Answer 2

Answer:

24

Step-by-step explanation:

We have f(x + 4) + f(x – 4) = f(x) ...(i) Replacing x by x + 4, we get, f(x + 8) + f(x) = f(x + 4) ...(ii) From (i) and (ii), we get, f(x + 8) + f(x + 4) + f(x – 4) = f(x + 4) ⇒ f(x + 8) + f(x – 4) = 0 Replacing x by x + 4, we get, f(x + 12) + f(x) = 0 ...(iii) Again replacing x by x + 12, we get, f(x + 24) + f(x + 12) = 0 ...(iv) Subtracting (iii) from (iv), we get, f(x + 24) + f(x + 12) – f(x + 12) – f(x) = 0 ⇒ f(x + 24) – f(x) = 0 ⇒ f(x + 24) = f(x) Thus f(x) is periodic with period 24