MATLAB: Solving a simple equation

syms sym

I have a function that can not be simplified further that goes something like this
0 = (1+exp(x))/(1+exp(-x))
(Simplified, my function is much longer and convoluted. The point is that I can't just write it as 'x = …')
How can Matlab approximate this equation by choosing a good value for x? What is the command for this?

Best Answer

If you are looking for a numerical solution, then this is a rootfinding problem. Use fzero, a tool designed to solve exactly that problem.
xfinal = fzero(@(x) (1+exp(x))./(1+exp(-x)),xstart);
You must supply a value for xstart. Better yet is if you can supply a pair of points that are known to bracket a solution.
Of course, this function has no solution, so it will always fail, but I assume that your true function does have one.
If you have truly tried to confuse things, and your real function is multi-dimensional, then you can use tools from the optimization toolbox. Here one would use fsolve.
If you are looking for a symbolic solution then solve (which requires the symbolic toolbox) is the answer.
Related Question