Question

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

• A. $-4$
• B. $4$
• C. Data Insufficient
• D. $0$

Answer 1

The correct option is D $0$

Since $f\left(x\right)$ is an odd periodic function with period $2$

$\therefore f\left(x\right)=-f\left(x\right)$ and $f(x+2)=f\left(x\right)$

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

and $f(-2)=f(-2+2)=f\left(0\right)$

Now $f\left(0\right)=f(-2)=-f\left(2\right)=-f\left(0\right)$

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