Solving single variable equation where other variables depends on that single variable

Is there a method to solve equations like :

lets say we first define a variable x initial value unknown and we know y = f(x) ; z = f(y) ; p = f(z).

Now the equation to be solved is like 250 = x + y + z where after solving we find x and we need the final value of p.

I have used iteration to solve this but that takes a long time. Any method would be appreciated.

Thanks

Answer 1

[Alan Stevens]

Try using fzero. For example:

f = @(x) x.^2 +1./x;   % arbitrary function: replace with your own

y = @(x) f(x);

z = @(x) f(y(x));

p = @(x) f(z(x));

g = @(x) x + y(x) +z(x) - 250;

% Initial guess
x0 = 1;

x = fzero(g, x0);

format long
disp([x, p(x)])

   1.0e+04 *

   0.000386468834515   5.333363091026294