Value Excluded from the Domain

Date: 5/23/96 at 21:36:35
From: Anonymous
Subject: Algebra II

f(x)=3x cubed + x squared - 2x over 9x squared -4
I have to find the value that is excluded from the domain.  
I don't even know where to start.

Date: 5/24/96 at 11:17:29
From: Doctor Ethan
Subject: Re: Algebra II

Hey Judy,

To represent cubed and squared I will use ^ :

     x cubed is x^3
and 
     x squared is x^2

So your problem is

        3x^3 + x^2 - 2x
f(x) = ------------------
           9x^2 - 4

Let's see what values of x will give us problems. With things like 
this there are usually only two things that can go wrong: f(x) can be 
imaginary (if you don't know what that means, ignore it), and f(x) can 
be undefined.

Problem one happens when we have the square root of a negative number.
Problem 2 happens when we have a fraction with zero in the 
denominator. Since we have no square roots in this problem let's look 
for problem 2.

Are there any values of x that will make the denominator 0?  In other 
words, we need to solve this equation:

     9x^2 - 4 = 0

That is,

     9x^2 = 4
or
     x^2 = 4/9

so   x = + or - 2/3

So those are the points that cannot be in the domain.

Good luck.

-Doctor Ethan,  The Math Forum
 Check out our web site!  http://mathforum.org/dr.math/