In this case the domain is
or in other words, the domain consists of of two intervals:
Parts 3-4
Deal with question 2.
The function acosh is double valued for any argument >1 ,
and single valued only for the argument =1 .
In this particular case the function is single valued for two values x=±1 .
Parts 5-7
Deal with question 3.
The function can be rewritten as:
In the case that ,
we know that
where the + sign is for the upper (y positive) branch of the acosh
and the − sign - for the lower (y negative) branch of the acosh .
In the case that
from part 6 and by applying the rules of differentiation one obtains
where the − sign is for the upper (y positive) branch of the acosh
and the + sign - for the lower (y negative) branch of the acosh .
Score
Correct solution of questions 1 and 2 gives credit of 2 points for each one.
Correct solution of question 3 gives credit of 6 points.
By parts:
parts 1,2,3,4 are worth 1 point each.
parts 5,6,7 are worth 2 points each.