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zmudz
 one year ago
Suppose that \(f(x)\) and \(g(x)\) are functions which satisfy \(f(g(x)) = x^2\) and \(g(f(x)) = x^3\) for all \(x \ge 1\). If \(g(16) = 16\), then compute \(\log_2 g(4)\).
(You may assume that \(f(x) \ge 1\) and \(g(x) \ge 1\) for all \(x \ge 1\).)
zmudz
 one year ago
Suppose that \(f(x)\) and \(g(x)\) are functions which satisfy \(f(g(x)) = x^2\) and \(g(f(x)) = x^3\) for all \(x \ge 1\). If \(g(16) = 16\), then compute \(\log_2 g(4)\). (You may assume that \(f(x) \ge 1\) and \(g(x) \ge 1\) for all \(x \ge 1\).)

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amistre64
 one year ago
Best ResponseYou've already chosen the best response.0hmm, will a substitution make life simpler

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I don't see the link between the given information and the question. :( if g(16) =16, then g(4) =4, and \(log_2 g(4) = log_2 4 =2\)

zmudz
 one year ago
Best ResponseYou've already chosen the best response.0I already tried 2, it's not 2. But a hint says that I should find g(4) first. I just don't know how.

Zarkon
 one year ago
Best ResponseYou've already chosen the best response.2\[f(g(4))=4^2=16\] \[g(f(g(4)))=g(16)=16\] \[g(f(g(4)))=[g(4)]^3\] so \[[g(4)]^3=16\] \[\cdots\]
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