I have a role $ f $ defined on $ (- 1.1) $.

The definition is sufficient for a minimal example

```
f(z_):=z^2 - 1
```

I have to find a list of points so that $ f (z_0) = f (z_1) $Dots whose picture is "on the same level".

I continued by finding the minimum above

```
min = First@Minimize(f(z), {z})
```

what occurs $ z $ equal

```
argmin = Values@Last@Minimize(f(z), {z})
```

I also made a list with

```
rang = Subdivide(a, 0,10)
```

over the range from the minimum to the predefined value.

Now I want to find points for each element of this list $ f (z_0) = f (z_1) = rang_j $for each element of the list.

I couldn't find a better plan than defining a list of functions $ fun_j = (f (z) + rang_j) ^ 2 $. By moving the original function and squaring I'm sure the functions $ fun_j $, one for each item in the list $ rang $ are positive everywhere except the roots.

I then wanted to go through the list of functions to a limited minimization via the commands (the argument) $ f_j $ Since I am only used to clarify my question, I understand that the sintax will actually be different. That is exactly what the question is about.

```
Minimize({f_j, z > argmin}, {z})
Minimize({f_j, z > argmin}, {z})
```

That is, two minimizations are performed, one to the left and one to the right of the $ {arg , min} $. I know for mathematical reasons that there are two unique solutions.

I create my list of functions as

```
f1(z_,c_):=f(z)+c
```

and then with

```
f1(z,rang)
```

But I have problems with minimizing iteration. Any suggestion would be helpful.

I'll try it

```
Minimize({f1( z, rang), z > b}, z)
```

returns an error message because the Minimize function argument is expected to be a scalar function.

I would also like to hear about better methods in general and related to Mathematica.

cheers