Question

If f(x)is an odd periodic function with period 2, then f(4) equals

• A. \N
• B. 2
• C. 4
• D. -4

Answer 1

The correct option is A \N

We have, f(-x) = -f (x) and f(x+2) = f(x)
$\therefore$ f(0) = f(0+2) = f (2)
Also f(0) = f(-2+2) = f (-2) = -f (2) = -f (0)
$\Rightarrow$ 2f(0) = 0 $\Rightarrow$ f(0) = 0
Now, f(4) = f(2+2) = f (2) = f (2) = f(0+2) = f (0) = 0