Question

If $f\left(x\right)+f(x+4)=f(x+2)+f(x+6)\forall xϵRanda>0$ and f(x) is periodic, then period of f(x), is

• A. 8
• B. 1
• C. 6
• D. 10

Answer 1

The correct option is A 8

$f\left(x\right)+f(x+4)=f(x+2)+f(x+6)...1\left(i\right)$.
Replacing x by x + 2 in equation (i), we get
$f(x+2)+f(x+6)=f(x+4)+f(x+8)$ . . . . .(ii)
Adding (i) and (ii) $f\left(x\right)=f(x+8)$
period of the function is 8