For a positive integer x, define f(x) such that f(x + a) = f(a × x), where a is an integer and f(1) = 4. If the value of f(1003) = k, then the value of ‘k’ will be:
Explanation:
f(1) = 4 f(2) = f(1+1) = f(1 × 1) = f(1) = 4 … Assume that f(n – 1) = 4 f(n) = f(1 + (n – 1)) = f(1 × (n – 1)) = f(n – 1) = 4 Thus, by induction principle, f(n) = 4, for all n. ∴ f(1003) = k = 4 Hence, option (e).
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