Update: André Zmuda has kindly taken the time to improve his original answer, and describe the improvements in comments. I've changed this summary to reflect that.
André Zmuda and Robin Betts
have each provided good answers using different approaches.
I would like to accept both answers but I can only accept one.
So I am upvoting both and accepting Betts' (for a reason that has since been corrected.)
Here I present each method, massaged slightly to be closer to the formulation of the $x = F(y)$ node group in the question. See the individual answers for more details.
I have made a slight change, introducing a Map Range math node so that the conditions $a \le u \le $b can be made apparent.
Zmuda's method uses an Accumulate Field Node to generate values in the range of 0 to (Value * the maximum index in the geometry). In this Node group the maximum index is controlled by the Count input of the Mesh Line node.
My small modification maps that range to the U range for the equation by using a Map Range node, as mentioned above.
Betts' example is actually a 3D curve, but Zmuda's method could generate a 3D curve by adding a Curve to Mesh node after the Set Position node.
As with Zmuda's method I have introduced a Map Range for the same reason. Betts' method uses a Curve Line rather than a Mesh Line. I have also added a Curve to Mesh Node after the Set Position node to give a closer similarity to the original node group. I also reduced his elegant 3D trefoil equation to a simple 2D circle to match the other examples.
Betts' method uses a Spline Parameter node to generate the $u$ values. The manual says this about the Factor output:
When the node is used on the point domain, the value is the portion of the spline’s total length at each control point. On the spline domain it is the portion of the curve’s total length at the start of the spline.
Similarities and differences
Both methods rely on some form of generator to create the u values. After that the math would be the same for a given function in either method. Zmuda's method works strictly with meshes; while Betts' opted for curves. Either would serve my purpose, since there are Mesh to Curve and Curve to Mesh nodes.
Bonus for reading this far:
Here is a blend file containing both methods; as modified by me to match the original example in the question. Update: I have edited the node group for Zmuda's method to incorporate the fix he gave in comments.