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NDA 1 2025 Maths, question 95

Topic: Algebra

Passage · Q95 to Q96

The function f(x)f(x) satisfies f(x/y)=f(x)/f(y)f(x/y) = f(x)/f(y) for all positive real values of xx and yy, and f(2)=3f(2) = 3.

Q95

What is f(16)f(16) equal to?

  1. (a) 18
  2. (b) 27
  3. (c) 54
  4. (d) 81Correct answer

Solution.

Answer: (d) 81

  1. Substitute x=4,y=2x = 4,y = 2: f(2)=f(4)/f(2)f(2) = f(4)/f(2), so f(4)=9f(4) = 9.
  2. Next use x=16,y=4x = 16,y = 4: f(4)=f(16)/f(4)f(4) = f(16)/f(4), so f(16)=92=81f(16) = 9^{2} = 81.