What exactly is this question acting?

[xdrgnh]

http://www.math.poly.edu/courses/ma0914/past_exams/MA922_Midterm_2001-05-23.pdf

The first questions that are asking about domain. If I recall right domain is the set which has all possible inputs for a function. I don't understand it means in this context.

Lol it wrote acting instead of asking.

 

[Mentallic]

Hmm yeah that does look odd. I suppose what it's supposed to be trying to say is within the domain of arcsin(x), is the value of arcsin(sin(-1)) = -1?

 

[xdrgnh]

Well then the answer would be yes because sin-1 is a number less then 1 and -1.

 

[Mentallic]

Well then the answer would be yes because sin-1 is a number less then 1 and -1.

Nearly, the arcsin function is taken to be the inverse of the sin function on the domain $$x\in \left[-\frac{\pi}{2},\frac{\pi}{2}\right]$$ and so because -1 is in this domain, then sin(-1) is defined and thus arcsin of that value is also defined, giving us back the value -1.