Largest Possible Value of f(1)

CAT 2017 Slot 2 · Quantitative Ability · Medium · Functions

This is a medium Quantitative Ability question from the CAT 2017 Slot 2 paper. It tests Functions. The full answer key and a step-by-step explanation are below — try it yourself first, then reveal the solution.

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If $f(ab) = f(a)f(b)$ for all positive integers $a$ and $b$ , then the largest possible value of $f(1)$ is

Answer

Explanation

Substitute $a = 1$ and $b = 1$ into $f(ab) = f(a)f(b)$ : $f(1) = f(1) \times f(1)$ $f(1)^2 - f(1) = 0 \implies f(1)(f(1) - 1) = 0$

Thus, $f(1) = 0$ or $f(1) = 1$ .

The largest possible value of $f(1)$ is 1.

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Largest Possible Value of f(1)

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