Functional Equation Value Evaluation

XAT 2015 · Quantitative Ability & Data Interpretation · Hard · Quantitative Ability

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For a positive integer $x$ , define $f(x)$ such that $f(x + a) = f(a \times x)$ , where $a$ is an integer and $f(1) = 4$ . If the value of $f(1003) = k$ , then the value of ' $k$ ' will be:

A.
1003
B.
1004
C.
1005
D.
1006
E.
None of the above

Answer

Explanation

$f(1003) = f(1002 + 1) = f(1002 \times 1) = f(1002)$ . Repeating this down to $f(1) = 4$ . Thus $k = 4$ , which is option E (None of the above).

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Functional Equation Value Evaluation

Explanation

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