If f (x) = (x+1) ^-1 and g (x) = x-2, what is the domain of f (x) divided by g (x)

F (x) = (x+1) ^-1

f (x) = 1 / (x+1) so

f (x) / g (x) is

1/[ (x+1) (x-2) ]

Since division by zero approaches infinity, it is not a real value, and is said to be undefined. Division by zero is "not allowed", which just really means that it does not have a real value. So in this case x cannot equal - 1 or 2 so the domain is:

All real numbers except - 1 or 2 ... which can be expressed as:

(-oo,-1), (-1,2), (2,+oo)