# range of elements

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• May 2nd 2010, 08:15 AM
alexandrabel90
range of elements
given that -x is an element of the set B where l x^2 - 3l <1. what is the range of values that are in the set B?
• May 2nd 2010, 08:56 AM
Pulock2009
solution
Quote:

Originally Posted by alexandrabel90
given that -x is an element of the set B where l x^2 - 3l <1. what is the range of values that are in the set B?

|x^2-3|<1
=>-1<x^2-3<1
=>2<x^2<4
=>sqrt(2)<x<2
therefore if x be any element of B the range of values that are in set B is given by (sqrt(2),2).
• May 2nd 2010, 08:57 AM
HallsofIvy
Quote:

Originally Posted by alexandrabel90
given that -x is an element of the set B where l x^2 - 3l <1. what is the range of values that are in the set B?

$\displaystyle |x^2- 3|< 1$ is the same as $\displaystyle -1< x^2- 3< 1$ and $\displaystyle 2< x^2< 4$. That gives B as the union of two separate intervals.
• May 2nd 2010, 09:04 AM
Pulock2009
please clarify
Quote:

Originally Posted by HallsofIvy
$\displaystyle |x^2- 3|< 1$ is the same as $\displaystyle -1< x^2- 3< 1$ and $\displaystyle 2< x^2< 4$. That gives B as the union of two separate intervals.

one interval is undoubtedly (sqrt(2),2).which is the other and how???
• May 2nd 2010, 09:09 AM
Plato
Quote:

Originally Posted by Pulock2009
one interval is undoubtedly (sqrt(2),2).which is the other and how???

$\displaystyle \left( { - 2, - \sqrt 2 } \right)$
• May 2nd 2010, 09:09 AM
alexandrabel90
is the other interval from (-2, sq rt 2)