What is the range for this function? g(x,y)=arcsin⁡(x/(x+y))

Question

I'm required to find the range of:

Answer 1

range of arcsin(c) = -90 to +90 degrees = -pi/2 to pi/2 radians

in contrast to

range of sin^-1(c) = -infinity to + infinity degrees

for any c including c=x/(x+y) except when x=-y or x=y=0

domain is -1 to +1 which means x </=x+y or x>/=x+y if x and y are opposite signs

Answer 2

Since the argument x/(x+y) can take any value for appropriately chosen x and y, the range of the function is the usual range of arcsin: [-pi/2, pi/2].