Question

Find the domain of the function. (Enter your answer using interval notation.)
f(x) = x+3/x^2-1

Answer 1

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