If f(x)= (x+1)^-1 and g(x)=x-2 what is thr domain of f(x)÷g(x)​

I hope this helps you

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) 

F(x)/g(x) is undefined where g(x) = 0. That occurs where x=2.

The domain is all real numbers except 2.
(-∞, 2) ∪ (2, ∞)

Step-by-step explanation:

Function g(x) = x - 2 is in the denominator.  We cannot divide by zero, so the domain of (f/g)(x) is x ≠ 2.

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