Need to solve f(x) in terms of g(x)

Sep 2009

I have two functions f(x) and g(x). They are both functions of x. When I plot the two functions on a graph, f(x) on the y-axis and g(x) on the x-axis, I get a continuous function.

I would like to solve f(x) in terms of g(x) so that I can have a formula for this continuous function I have plotted.

Here are the two functions.

f(x)=\frac{Nx^2}{4q}\left ( \frac{4z^2\cos{\left(\frac{n\pi\ln\frac{x}{k}}{z}\right)}-2n\pi z\sin{\left(\frac{n\pi\ln\frac{x}{k}}{z}\right)}}{4z^2+n^2\pi^2}+1\right )+\frac{Nx}{2}\left( \cos{\left(\frac{n\pi\ln\frac{x}{k}}{z}\right)}+1\right)

\(\displaystyle g(x)=\frac{Nx}{2q}\left ( \frac{z^2\cos{\left(\frac{n\pi\ln\frac{x}{k}}{z}\right)}+n\pi z\sin{\left(\frac{n\pi\ln\frac{x}{k}}{z}\right)}}{z^2+n^2\pi^2}+1\right )+\frac{N}{2}\left( \cos{\left(\frac{n\pi\ln\frac{x}{k}}{z}\right)}+1\right )\)

The only variable is x. The rest of the letters are constants.

I don't really expect anyone to solve the problem for me, but if you could give me some suggestions that would be great, or even just tell me that it is even at all possible to solve with the given information.

Thank you