I've whittled it down to:

y = (e^x+1)/2

and y = (-e^x-1)/2

For positive and negative takes on the absolute value, but which do I choose?

What's more, as it says "state the rule", should I present my answer as f^-1-infinity,a), etc? Presenting the entire rule like they do in the question?

Oh, and also, in the previous question we worked out a = 1/2.