f(x)=(x+3)/(x^2-1)

Question

I have to find the domain and put it into interval notation.

Answer 1

Molly, the domain is defined as any value x can possibly take.

f(x) = (x + 3)/(x²-1)

 

The only thing you absolutely cannot do is divide by 0. To find out what that would be, all you do is set the denominator to 0 and solve for x:

x² - 1 = 0

x² = 1

x = √1

x = ± 1

That means that x cannot equal -1 or 1. All other numbers are included. In interval notation that is shown like this:

(-∞,-1)∪(-1,1)∪(1,∞)

 

Answer 2

The Domain is going to be ALL Real Numbers less what x cannot be in the denominator. So, set the denominator equal to zero and solve.

 

(x^2-1) is a difference of two squares and factors to: (x-1) (x+1) therefore, x cannot = 1

 

In Interval notation you find:

 

D: (-00, -1)U(-1,1)U(1,00)

 

So, neg infinity to -1, -1 to 1 and 1 to pos infinity. Note that there are asymptotes at X=1, -1 so you use () on those two numbers. You also use () on infinity as it never reaches it.

 

Hope that helps,

 

Teodor M.