Examples of bounded, positive, inverse demand curves
You can find demand functions like this in textbook and exam problems. Just a random example from internet:
$$Q = \ln 4 - 0.5 \ln P$$
which is just a special case of $Q=−1/a \ln (P/b)$ where a is 1 and b is also 1 and there is some additional constant $\ln 4$. We just had an exam where I also saw one of the other examples. If I remember right it was $Q = \frac{100}{P}-1$. I also remember seeing more of them in textbooks but it would take forever to find them in thick book full of math problems.