Expert: Paul Klarreich - 2/1/2012

Question
What is the domain of the following in interval notation? (square root of 5x-2) / (x^2-4). I think it's (negative infinity, 2) and (2, infinity) but I'm not sure. This is what I do not understand.

Answer
Questioner:Hiral
Country:New Jersey, United States
Category:Calculus
Private:Yes    <<<<<<<<<<<<<<<<<<< changed
Subject:Domain

Question:

What is the domain of the following in interval notation? (square root of

5x-2) / (x^2-4). I think it's (negative infinity, 2) and (2, infinity) but

I'm not sure. This is what I do not understand.
...................................................
       sqrt(5x - 2)
f(x) = --------------
        x^2 - 4

When you have a function specified algebraically, the domain is always:

D = { all real numbers that don't cause trouble }

Trouble? Could be:

A-bad. a square root of a negative number.

B-bad. a fraction with 0 in the denominator.

So you need  5x - 2 >= 0, or you get an A-bad.

5x - 2 >= 0

5x >= 2

x >= 2/5   << use this
......................

Also you need x^2 - 4 /= 0,  or  x /= +-2   << use this,too.
......................
Put those 'use this'-s together to get your intervals.