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$Let f : N \to N where N is set of natural numbers be a function such that f (x + y) = f (x y) \forall x \geq 4 and y \geq 4, then$

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$f (4) = f (5)$

$f (8) = f (9)$

$f (5) = f (6)$

$f (7) = f (8)$

answer is C.

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Detailed Solution

$\begin{array}{l} f (1 + f (1)) = 4 f (1) \\ \Rightarrow f (1 + 4) = 4 \times 4 \\ \Rightarrow f (5) = 16 \\ Now f (5 + f (5)) = 4 f (5) \\ \Rightarrow f (5 + 16) = 4 \times 16 \Rightarrow f (21) = 64 \end{array}$

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