Question

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

• A. $0$
• B. $2$
• C. $4$
• D. $-4$

Answer 1

The correct option is A $0$

Given f(x) is an odd period function period function

$\to f(-x)=-f\left(x\right)$ and f(0)=0

since f(x) has period 2.

$\therefore f\left(0\right)=f\left(2\right)=f\left(4\right)=0$

Hence f(4)=0