Question

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

Accepted Answer

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

Functional Equation Value Evaluation

Explanation

Practise this under exam conditions