XAT 2015 — QA & DI Question 17
Basics (Functions)Easy
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:
Answer & solution
- A
1003
- B
1004
- C
1005
- D
1006
None of the above
Solution
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).