# Stating Domain

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• Feb 4th 2010, 03:36 PM
blueknightdrummer
Stating Domain
Ok, we are in our pre-req. chapter and i know i should already know this but its been awhile since i have had any math so could someone please explain how to state the domain of a function and the basis behind it? (i know it kinda looks something like this--> {X/ x>or= -2}) Thanks!
• Feb 4th 2010, 09:41 PM
MollyMillions
The domain of a function f(x) is all the values of x for which the function is defined. So, if you plug a value into the function that isn't in the domain, you'll get something undefined (dividing by zero, square root of a negative number, etc.).

The notation you're talking about is set-builder notation.

{ x | x >= 2 }

Since f(x) is a function of x, the domain is values of x (hence the first variable). The vertical bar is read "such that". After the vertical bar are the allowed values of x (the domain). So this function is undefined for values of x less than 2.

For example, the function $\frac{1}{\sqrt{x-2}}$ has the domain {x | x =/= 2 } because x=2 would be dividing by zero.
• Feb 5th 2010, 02:57 AM
HallsofIvy
Quote:

Originally Posted by MollyMillions
The domain of a function f(x) is all the values of x for which the function is defined. So, if you plug a value into the function that isn't in the domain, you'll get something undefined (dividing by zero, square root of a negative number, etc.).

The notation you're talking about is set-builder notation.

{ x | x >= 2 }

Since f(x) is a function of x, the domain is values of x (hence the first variable). The vertical bar is read "such that". After the vertical bar are the allowed values of x (the domain). So this function is undefined for values of x less than 2.

For example, the function $\frac{1}{\sqrt{x-2}}$ has the domain {x | x =/= 2 } because x=2 would be dividing by zero.

Assuming you are talking about real valued functions, the domain would be $\{x| x> 2\}$ so that we are not taking the square root of a negative number.