How to get the inverse function when it's only 1-1 in certain range?

I have a function f which is not one to one globally, but it is so on [0,1]. Now I want to compute the inverse function g of f on [0,1]. But finverse gives me the part on the range I don't need. How to deal with it? Below is the example:

phi=@(m,z)m*z^(m-1)-(m-1)*z^(m); 
phi2=@(z)phi(2,z);
iphi2=matlabFunction(finverse(phi2(z)))

Answer 1

[Star Strider]

I would just use fzero instead.

If ‘phi_d’ is your desired value and you want to see what value of ‘z’ produces it, this works:

phi_d = 0.5;
z_inv = fzero(@(z) phi2(z)-phi_d, 0.1);

Here, ‘z_inv’ is about 0.293.

Answer 2

[Roger Stafford]

As you have defined iphi2 it is simply one of the two solutions to a quadratic equation:

   z = 1-sqrt(1-phi2)