What is f(16) equal to?
Consider the following for the two (02) items that follow : The function f(x) satisfies f(\frac{x}{y})=\frac{f(x)}{f(y)} for all positive real values of x and y, and f(2)=3.
- A. 18
- B. 27
- C. 54
- D. 81 ✓
Correct Answer: D. 81
Explanation
The given property implies f(x) is of the form x^k. Since f(2) = 2^k = 3, we want to find f(16) = 16^k = (2^4)^k = (2^k)^4. Substituting 2^k=3, we get 3^4 = 81.
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