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How would solve for k in a function such as the following $j=9k+2k(k^{2k+1})$? I only know up to very basic calculus and am unsure that with that amount of knowledge it is possible. Is there a book or site I could look at to understand more about expressing complex function?

Note: I am aware the name is very vague so if anyone as any suggestions for an edit let me know.

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    $f(k)=9k+2k(k^{2k+1})$ is already a function of $k$ (not sure why that $j$ is in there).2012-02-11
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    Sorry I wasn't thinking. I said I want it to be a function of j but what I am looking for is to plug in a number for j and and get a k rather then the opposite so I am not sure if I wrote i correctly above. Does that make sense?2012-02-11

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A more usual way of expressing what you were trying to express would be how to solve the equation for $k$, or how to write $k$ as a function of $j$ such that the equation is satisfied.

The answer is that I don't think you can. This is often the case when the variable to be solved for appears both in an exponent and elsewhere; in some such cases you can use the Lambert W function, but I don't see how that could help you here.

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    I rephrased the question, hopefully, appropriately. That's what I thought but it seems, unless I am grossly mistaken, graph-able which would seem to support their being a function or some manner of describing it.2012-02-11
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    @Jesse: It's certainly graphable, and for $k\gt0$ it's also bijective so that $k$ can be regarded as a function of $j$, but that doesn't mean that you can explicitly solve for $k$. The difference is between knowing in general that $k$ is a function of $j$ in the sense that one value of $k$ corresponds to each value of $j$ (for $j\gt0$), and obtaining an expression for that function in terms of well-known simple functions.2012-02-11
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    So then how would you express it if you wanted a computer or some machine to graph it?2012-02-13
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    @Jesse: The graph of $k$ as a function of $j$ is the graph of $j$ as a function of $k$ with the $j$ and $k$ axes swapped. So you can just let the machine do whatever it would do to graph $j$ as a function of $k$, but with $j$ values used as horizontal coordinates and $k$ values used as vertical coordinates instead of the other way around.2012-02-13