By signing in you confirm you are 18 or older, or have your parent’s or guardian’s consent.

NDA 1 2025 Maths, question 96

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.

Q96

What is f(1)f(4)f(1)f(4) equal to?

  1. (a) 4
  2. (b) 8
  3. (c) 9Correct answer
  4. (d) 18

Solution.

Answer: (c) 9

  1. Put x=y=2x = y = 2 to get f(1)=f(2)/f(2)=1f(1) = f(2)/f(2) = 1.
  2. With x=4,y=2x = 4,y = 2, f(4)=f(2)2=9f(4) = f(2)^{2} = 9.
  3. Therefore f(1)f(4)=1×9=9f(1)f(4) = 1 \times 9 = 9.