I have a function $ f $ defined in $ (- 1,1) $.

For a minimal example, it is sufficient to define

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

I need to find a list of points so that $ f (z_0) = f (z_1) $, points whose image "is at the same height".

I continued to find the minimum through

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

what happens for $ z $ equal to

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

Also I created a list with

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

spanning the range from minimum to predefined value.

Now I would like to find, for each item on this list, points such that $ f (z_0) = f (z_1) = rang_j $, for each item in the list.

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

So I wanted to iterate over the list of functions a restricted minimization through the commands (the argument $ f_j $ just to clarify my question, I understand that the syntax will be different, that's exactly what the question is about):

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

that is, run two minimizations one on the left and one on 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 using

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

but I find it hard to iterate Minimize, any suggestion would be helpful.

Annoying

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

produces an error message, since the Minimize function argument is expected to be a scalar function.

I'd also like to hear about better methods, in general and in reference to Mathematica.

Health