Question

Let f : N→ 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 :

(1) 6 

(2) 54 

(3) 18 

(4) 36

Answer 1

Correct answer is: (2) 54

ƒ(m + n) = ƒ(m) + ƒ(n)

Put m = 1, n = 1 

ƒ(2) = 2ƒ(1) 

Put m = 2, n = 1 

ƒ(3) = ƒ(2) + ƒ(1) = 3ƒ(1)

Put m = 3, n = 3 

ƒ(6) = 2ƒ(3) 

\(\Rightarrow\) ƒ(3) = 9 

\(\Rightarrow\) ƒ(1) = 3, ƒ(2) = 6 

ƒ(2).ƒ(3) = 6 × 9 = 54