Question 68

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:

Solution

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Expression : $$f (x + a) = f (a \times x)$$

Also, $$f(1) = 4$$

Now, $$f(1003) = f(1002 + 1) = f(1002 \times 1) = f(1002)$$

Similarly, $$f(1002) = f(1001) = f(1000) = ......... = f(1) = 4$$

$$\therefore f(1003) = k = 4$$

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