Question
Download Solution PDFLet f(x) f(y) = f(xy) for all real x, y. If f(2) = 4, then what is the value of f(1/2)?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFExplanation:
Given:
f(x)f(y) = f(xy)
Let f(x) = xn and f(y) = yn .
⇒f(xy) = (xy)n
f(2) = 4
⇒ 4 = (2)n
⇒ n= 2
\(f(\frac{1}{2}) =( \frac{1}{2})^2 =\frac{1}{4}\)
∴ Option (a) is correct.
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