CAT Quant Practice Problems

Question: Let f(x) be a function satisfying \(f(x)\times f(y) = f(xy)\) for all real x, y. If f(2) = 4, then what is the value of \({\rm{f}}\left( {\frac{1}{2}} \right)?\)
  1. 0
  2. \(\frac{1}{4}\)
  3. \(\frac{1}{2}\)
  4. 1
  5. cannot be determined

Correct Option:2

$f(1)^2$ = f(1) => f(1) = 1

f(2)×(f(1/2) = f(1) => 4x = 1

So, f(1/2) = 1/4


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