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### 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

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/
```
Associated Topics:
High School Basic Algebra
High School Equations, Graphs, Translations

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