Domain of a Function

Date: 9/13/96 at 2:24:1
From: Bill Spoth
Subject: Function Analysis

Dr. Math,

I need help. 

Let f be the function given by f(x)= x/sqrt(x^2 - 4). What is the 
domain of f(x)?

Thanks, Dr. Math! Sincerely,
   Troubled Math Student

Date: 9/13/96 at 9:15:16
From: Doctor Leigh
Subject: Re:  Function Analysis

Thank you for your question.  

To find the domain of any function you look for areas where the 
function is undefined.  This normally includes negatives under 
radicals and zeros in the denominator of a fraction.  

Here we would have a zero in the denominator if x^2-4 = 0.  We then 
solve for x and see that if x is either positive or negative 2 the 
function will be undefined.  

We are also dealing with a radical.  To get a negative under the 
radical sign we set x^2-4 < 0. Solve the equation for x and you get 
x < 2, x > -2.  So the domain of this function is negative 
infinity to -2 (non-inclusive) and 2 to infinity (non-inclusive)

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