Largest Possible Value of f(1)

CAT 2017 Slot 2 · QA · Medium · Functions

All CAT 2017 Slot 2 questionsMore Functions questionsAll CAT QA

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

Answer

1

Explanation

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

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

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

Practise this under exam conditions

Sign in to solve it with a live timer, the on-screen CAT calculator, and streak and accuracy tracking across every question you attempt.

Solve in the workspace