CAT 2017 Functions Question (Hard)

Question

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

Accepted Answer

Step 1 We are given f ab f a f b for all positive integers a and b. This is a multiplicative function. Step 2 Put a b 1 Then f 1 1 f 1 f 1 f 1 f 1 Solving f 1 f 1 0 f 1 f 1 1 0 f 1 0 or f 1 1 We want the largest possible value of f 1 , so Final Answer f 1 1

CAT 2017

Quantitative

Functions

Hard

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

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