New to Maths Stack Exchange. So I have these two peculiar functions:
$$x=L_c\left[\operatorname{coth}\left(2 \beta F L_p\right)-\left(2 \beta F L_p\right)^{-1}\right]\left(1+\frac{F}{K}\right)$$
$$ x=L_c\left[1-\frac{1}{2}\left(\beta F L_p\right)^{-1 / 2}+\frac{F}{K}\right] $$
Which I am trying to find hard time finding the inverse of each of these i.e finding F(x) instead x(F) as given in these equations.
Are there any tips? I do recognize that first question might be Transcendental equation thus I would assume approximation would be a better approach (with taylor expansion on trig identity ?).
I am trying to do curve fitting of the inverse of these functions to determine the parameters of $L_c$ $L_p$ and K. $\beta$ is given.