Answer:
The domain is:
In interval notation:
(-infinity,-1) U (-1,1) U (1,infinity)
In inequality notation: x<-1 or or -1<x<1 or x>1
The problem:
Find the domain of f(x) = (x+3)/(x^2-1)
Explanation:
The only thing that needs worrying here is the fraction since you can't divide by 0.
So if we solve x^2-1=0 we will find what x cannot be and everything else will be in the domain of the function.
Lets solve:
x^2-1=0
Add 1 on both sides:
x^2=1
Take square root of both sides:
x=1,-1
So the domain is all real numbers except x=-1,x=1.
The domain is:
In interval notation:
(-infinity,-1) U (-1,1) U (1,infinity)
In inequality notation: x<-1 or -1<x<1 or x>1