How to solve an equation with piecewise defined function?

Hi, I have been working on solving some equation in a more complicated context. However, I want to illustrate my question through the following simple example.

Consider the following two functions:

    %%%%%%%%%%%%%%%%%%%%%
    function y=f1(x)
        y=1-x;
    end

    %%%%%%%%%%%%%%%%%%%%%
    function y=f2(x)
       if x<0
           y=0;
       else
           y=x;
       end
    end
    %%%%%%%%%%%%%%%%%%%%%

I want to solve the following equation: f1(x)=f2(x). The code I used is:

    syms x;
    x=solve(f1(x)-f2(x));

And I got the following error:

    " ??? Error using ==> sym.sym>notimplemented at 2621

    Function 'lt' is not implemented for MuPAD symbolic objects.

    Error in ==> sym.sym>sym.lt at 812
            notimplemented('lt');

    Error in ==> f2 at 3
    if x<0  "

I know the error is due to that x is a symbolic variable and therefore I could not compare x with 0 in the piecewise function f2(x).

But is there any way to fix this and solve the equation?

Thanks a lot!

Answer 1

[Roger Stafford]

Instead of using 'solve' you can use 'fzero' for this problem. Of course this problem is so simple you can do it in your head, namely, a single solution at x = 1/2. However in general 'fzero' can prove useful in solving problems where the function is defined piecewise, provided it is continuous. Those in your example are continuous. For functions with a jump discontinuity, 'fzero' could be "thrown for a loop" - that is, unable to find a solution.

[Willow]

I used fsolve instead of solve. Then the problem disappears even if the function is defined piece-wise.