Question

A function $f$ satisfies the relation $f\left(n^2\right)=f\left(n\right)+6$ for $n\ge 2$ and $f\left(2\right)=8$. Then, the value of $f\left(256\right)$ is

• A. $24$
• B. $26$
• C. $22$
• D. $28$
• E. $32$

Answer 1

Answer: (B)

$26$

Given that, $f\left(n^2\right)=f\left(n\right)+6$

On putting $n=2$, we get
$f\left(4\right)=f\left(2^2\right)=f\left(2\right)+6=8+6=14$ $[\because f\left(2\right)=8]$

On putting $n=4$, we get
$f\left(16\right)=f\left(4^2\right)=f\left(4\right)+6=14+6=20$

On putting $n=16$, we get
$f\left(256\right)=f\left({16}^2\right)=f\left(16\right)+6=20+6=26$