Interesting challenge. The spec seems complete to me, but I can imagine it being easy to make an incorrect assumption because "Convert" could lead to some people assuming that $f(x)$ is expressing $x$ as a binary fraction. Would it be worth stating explicitly that this is in general impossible so people have an idea of what they are getting into before they start?

(Alternatively maybe something other than "Convert" in the title, such as "Bijection from"?)

The new title more than covers it. I like it.

Not really. Now it's even more unclear to me than before. What does it mean for a function to be "from rational numbers", for example. It would help if you explained what you wanted in plain English.

This is a very mathematical challenge. I wouldn't expect most people who write code to understand it, so its target audience will be people who enjoy both golfing code and mathematics.

The previous title sounded like a straightforward conversion challenge, which could attract people who don't have the background knowledge to attempt it. The new title sounds unapproachable to people not familiar with the mathematics, which gives a more accurate impression of the challenge.

Having said that, for people who don't yet know the terms but are interested in learning before considering trying the challenge, it might be worth making the first mention of the rational numbers a link to somewhere like Wikipedia.