Question

Find the period of the function satisfying the relation $f\left(x\right)+f\left(x+3\right)=0\forall x\in R.$

Answer 1

Answer: 6

Given $f\left(x\right)+f\left(x+3\right)=0$
Replace $x$ by $x+3$
Therefore, $f\left(x+3\right)+f\left(x+6\right)=0$
From $\left(1\right)$ and $\left(2\right)$ ,
$f\left(x\right)=f\left(x+6\right)$
Hence, the function has period $6$