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CAT 2017 Slot 2 — QA Question 31

Basics (Functions)Easy

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

Answer & solution

Answer: 1

Solution

Let f(1) = x

Suppose f(1 × 1) = f(1) × f(1)
∴ f(1) = f(1) × f(1)
⇒ x = x × x
⇒ x2 = x
⇒ x = 1 or x = 0

But the highest value of x = 1

Hence, 1.

CAT 2017 Slot 2 QA Q31: If f(ab) = f(a)f(b) for all positive integers a and b, then the largest possible value of f(1) is — Solution | TheCATExam