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Hello.
The reason is simple.
You have reached the inequality:
x squared >= 2
But that does not imply :
x >= +-sqrt(2)
Instead, it implies that x is a number, which when squared exceeds 2.
Therefore, the statement
x squared >= 2
actually reduces to:
x >= +sqrt(2) or x <= -sqrt(2)
-Vishvas Vasuki
sean_in_cali@xxxxxxxxx wrote:
> I was helping a student with her homework, then I got confused.
>
> here's the picture.
> http://img205.imageshack.us/img205/9510/domainih5.jpg
>
> Define the domain for a composite function f ( f (x) )
>
> if f (x) = sqrt ( x^2 -1 )
>
> then
>
> f ( f (x) ) = sqrt [ ( sqrt(x^2 -1) )^2 - 1 ]
>
> so,
>
> (sqrt (x^2 - 1) )^2 - 1 >= 0
>
> solving this, I get
>
> x>= +/- sqrt(2)
>
> This is where I got stuck.
>
> I forgot how to do inequalities like this...
>
> the domain obviously is...
>
> -sqrt (2) >= x >= sqrt (2)
>
> I just can't remember for the life of me what rule in inequality gives
> that...
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