Question

If $f\left(x\right)$ satisfies the relation $f\left(x\right)+f\left(x+4\right)=f\left(x+2\right)+f\left(x+6\right)$. For all $x$. Then period of $f\left(x\right)$ is

• A. $8$
• B. $4$
• C. $6$
• D. $2$

Answer 1

Answer: (A)

$8$

$f\left(x\right)+f(x+4)=f(x+2)+f(x+6)$ _(1)

$putx=x+2$

$f(x+2)+f(x+6)=f(x+4)+f(x+8)$

Put in (1)

$f\left(x\right)+f(x+4)=f(x+4)+f(x+8)$

$f\left(x\right)=f(x+8)$

the period is $8$

$A$ is correct.