Question

Let $f:N\to N$ be a function such that $f(m+n)=f\left(m\right)+f\left(n\right)$ for every $m,n\in N.$ If $f\left(6\right)=18,$ then $f\left(2\right)\cdot f\left(3\right)$ is equal to

• A. $54$
• B. $18$
• C. $6$
• D. $36$

Answer 1

The correct option is A $54$

$\because f(m+n)=f\left(m\right)+f\left(n\right),f:N\to N$
$\therefore f\left(x\right)=kx$
$\because f\left(6\right)=18\Rightarrow 18=k\cdot 6\Rightarrow k=3$
$\therefore f\left(x\right)=3x$
$\therefore f\left(2\right)\cdot f\left(3\right)=6\times 9=54$