# Find the range of a univariate function over a specific interval of the variable

I would like to find the range of the function below, but only for values of $$a$$ strictly greater than zero.

`v(a_)=-a*Log(1-(a - a E^(-1 - 1/a + ProductLog(E^(1 + 1/a))))/a)`

In other words: what is the range of $$v(a)$$, for/conditional on $$a>0$$ (reals).

• I have tried this: (ie without restricting)
`FunctionRange(v(a), a, y)`, but the computation time is too long, I can’t manage to get an output.

• I also have tried to define the $$v(a)$$ function over the domain that interests me using this:

`v(a_ /; 0 < a) := -a*Log(1-(a - a E^(-1 - 1/a + ProductLog(E^(1 + 1/a))))/a)` (solution found here), and then `FunctionRange(v(a), a, y)`, but the computation time seems to bee stil too long. Probably due to the fact that my restricted definition doesn’t seem to have worked: even in that case, `FunctionDomain(v(a),a)`returns $$a≠0$$ (instead of $$a>0$$ as I would have expected since it is what I defined in the first place).

EDIT

• This doesn’t seem to work either: `Assuming(a>0,FunctionRange(v(a), a, y))`.