How to create a function with an algebraic input

I am currently trying to create a function of the form

 g(f,x0,epsilon)

where f is an algebraic expression in terms of some symbols x. Specifically, I am using this in a function that takes in an arbitrary function f and approximates a solution to the equation f(x)= x within accuracy epsilon (if possible in sufficiently few steps), starting point x0.

Since f is arbitrary, I am required to define it in my code before i can compute f(x) for an arbitrary numerical input. I attempted this by the following: First I create a function called f:

function [f] = f( y )

   f = @(x)(y);
end

Then my function g is of the form

g(y, x0 , epsilon)

Where y is an algebraic expression in x. But this fails as when entering any algebraic expression it comes up with 'Undefined function or variable 'x'.'.

Any help is appreciated.

[James Tursa]

To be clear, the "y" above in your "f" function is a symbolic expression in terms of the symbol "x"? And you want to solve f(x)=x numerically to within some tolerance?

[Evgeny]

Yep, that is my goal.

Answer 1

[JESUS DAVID ARIZA ROYETH]

you can do like this:

function f=g(y, x0 , epsilon)
y=str2func(['@(x) ' y]);
%your code

but your input "y" need single quotation marks ( ' ) around them. for example : g('x+1',4,0.01)

Answer 2

[James Tursa]

Not really sure what you need, but here are a couple of examples:

Solving with symbolic expression:

>> syms x
>> f = cos(x)
f =
cos(x)
>> S = solve(f-x)
S =
0.73908513321516064165531208767387
>> subs(f,S)
ans =
0.73908513321516064165531208767387

Creating a function handle that you can use with your own numeric solver:

>> fhandle = matlabFunction(f-x)
fhandle = 
    @(x)-x+cos(x)