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

1

From CAT 2017 – Quantitative Aptitude – Algebra – Functions, we can see that,

Let us take the case when a=b=1

So, f(1) = f(1) f(1)

f(1) = [f(1)]^2

f(1)[f(1)-1] = 0

f(1) = 1

So, the maximum value of f(1) = 1

Answer: 1

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