```
FunctionRange({-a*
Log(1 - (a - a E^(-1 - 1/a + ProductLog(E^(1 + 1/a))))/a),
a > 0}, a, y)
```

`5.14988*10^-9 <= y <= 0.5`

and warming message:

Unable to find the exact range. Returning bounds on the range

computed using numeric optimization methods

So we have to consider `Derivative`

```
FunctionRange({D(-a*
Log(1 - (a - a E^(-1 - 1/a + ProductLog(E^(1 + 1/a))))/a), a) //
Evaluate, a > 0}, a, y)
```

`y > 0`

It means that `v(a)`

is a monotonic function ! So we just need to calculate the `Limit`

just as @Akku14 have done.

```
Limit(-a*Log(1 - (a - a E^(-1 - 1/a + ProductLog(E^(1 + 1/a))))/a),
a -> 0, Direction -> "FromAbove")
Limit(-a*Log(1 - (a - a E^(-1 - 1/a + ProductLog(E^(1 + 1/a))))/a),
a -> ∞)
```

0

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