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  4. Let f: N arrow N be a function such that f ( m + n )= f ( m )+ f ( n ) for every m , n ∈ N. If f (6)=18 then f(2) ⋅ f(3) is equal to :

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

JEE MainJEE Main 2021Relations and Functions - Part 2

Solution:

$f( m + n )=f( m )+f( n )$
Put $m =1, n =1$
$f(2)=2 f(1)$
Put $m =2, n =1$
$f(3)=f(2)+f(1)=3 f(1)$
Put $m =3, n =3$
$f(6)=2 f(3) \Rightarrow f(3)=9$
$\Rightarrow f(1)=3, f(2)=6$
$f(2) \cdot f(3)=6 \times 9=54$