Question

Find the domain of f(x,y)=sin^-1[(x-y)^2]. Do this mathematically and then describe the domain in words or with a sketch.

Answer 1

(x-y)^2<1

Answer 2

can you explain any?

Answer 3

you cannot take the arcsine of a number less than -1 or greater than one
so your answer is
\[-1\leq (x-y)^2\leq 1\] but of course
\[(x-y)^2\geq 0\]

Answer 4

this says the distance between x and y has to be less than or equal to one, and the graph is the region between two parallel lines
here is a picture
http://www.wolframalpha.com/input/?i=%28x-y%29^2%3C1