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CAT 2008 — QA Question 7

Basics (Functions)Easy
Passage / Data

Directions for next 2 questions:

The figure below shows the plan of a town. The streets are at right angles to each other. A rectangular park (P) is situated inside the town with a diagonal road running through it. There is also a prohibited region (D) in the town.

Let f(x) be a function satisfying f(x) × f(y) = f(xy) for all real x, y. Let f(2) = 4, then what is the value of f(12)?

Answer & solution

  • A

    0

  • 14

  • C

    12

  • D

    1

  • E

    Cannot be determined

Solution

Given, f(x) × f(y) = f(xy)

Let x = 1 and y = 2

∴ f(1) × f(2) = f(2)
∴ f(1) = 1

Now, let x = 1/2 and y = 2

∴ f(1/2) × f(2) = f(1/2 × 2) = f(1)

∴ f(1/2) × 4 = 1

∴ f(1/2) = 1/4

Hence, option (b).

CAT 2008 QA Q7: Let f(x) be a function satisfying f(x) × f(y) = f(xy) for all real x, y. Let f(2) = 4, then what is the — Solution | TheCATExam