Question

If$f:R\to R$ is a function satisfying the property
$f(x+1)+f(x+3)=K$, $x\in R$ then the period of $f\left(x\right)$ is

• A. $4$
• B. $K$
• C. $1$
• D. $\pi$

Answer 1

Answer: (A)

$4$

Given $f(x+1)+f(x+3)=K..\left(1\right)$

Replace $x\to x+2,$

$f(x+3)+f(x+5)=K......\left(2\right)$

From (1) & (2) $f(x+5)=f(x+1)$

Again replace $x\to x-1$

$\Rightarrow f(x+4)=f\left(x\right)\Rightarrow$ Period of given function is $4$.