Q. If $f(x)$ is an odd periodic function with period 2, then $f(4)$ equals
A) 0
B) 2
C) 4
D) -4
Explanation
(a)
Since, $f( - x) = - f(x)$ and $f(x + 2) = f(x)$
$\therefore\ \ \ f(x) = f(0)$ and $f( - 2) = f( - 2 + 2) = f(0)$
Now, $f(0) = f( - 2) = - f(2) = - f(0)$
$\Rightarrow 2f(0) = 0\ \ \Rightarrow \ \ \ \ f(0) = 0$
$\therefore\ \ \ f(4) = f(2) = f(0) = 0$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.