Let f : N [] N be a function such that f(m + n) = f(m) + f(n) for every m, n[]N.

Question

Let f : N $$\to$$ 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) . f(3) is equal to :

Accepted Answer

f(m + n) = f(m) + f(n)

Put m  = 1, n = 1

f(2) = 2f(1)

Put m = 2, n = 1

f(3) = f(2) + f(1) = 3f(1)

Put m = 3, n = 3

f(6) = 2f(3) $$\Rightarrow$$ f(3) = 9

$$\Rightarrow$$ f(1) = 3, f(2) = 6

f(2) . f(3) = 6 $$\times$$ 9 = 54

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