Skip to main content

2008/09 AHSMC Part 1 Problem 4

Problem 4 of 16

Let ff and gg be functions such that f(x)=g(2x)f(x) = g(2x) and g(x)=2f(x)g(x) = 2f(x) for all real numbers xx. If g(2)=3g(2) = 3, the value of f(12)f\bigl(\dfrac{1}{2}\bigr) is

Answer choices

Show solution

Solution

Note that f(x)=3xf(x) = \dfrac{3}{x} and g(x)=6xg(x) = \dfrac{6}{x} satisfy the hypothesis. In any case, we have f(12)=g(1)=2f(1)=2g(2)=6f\bigl(\dfrac{1}{2}\bigr) = g(1) = 2f(1) = 2g(2) = 6. The answer is (E).

University of Alberta