Question

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

• A. $0$
• B. $2$
• C. $-2$
• D. data is insufficient

Answer 1

The correct option is A $0$

Property of odd function is
$f(-x)=-f\left(x\right)\Rightarrow f\left(0\right)=0$
$f\left(x\right)$ has period 2,
$\therefore f\left(x\right)=f(x+2)$
$x\to -x$
$f(-x)=f(-x+2)$
$-f\left(x\right)=-f(x+2)=f(-x+2)$
$x=2,f\left(4\right)=-f\left(0\right)$
$f\left(4\right)=0$