Given f(x)=65 and f(x)f(1/x)=f(x)+f(1/x)... find the value of f(6)=???
There is not enough information here for the problem to have a unique solution. I suspect that the intended answer is that , and so f(6) = 217. But in fact if g(x) is an arbitrary function such that g(1/x) = g(x) and g(4)=3, then is a solution, and f(6) can be a completely arbitrary number greater than 1.
The equation can be written as So if then . There are very many functions having that property, but the most obvious solutions are for some fixed k.
If then . That suggests that we should take k=3, giving and hence
But as I said in the previous comment, there is nothing unique about that solution. If there really was no further information given, then this is a very badly thought out problem.