Function: Find the range of the funtion

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To find the range of the function given, one approach is to set the expression 2x/sqrt(x^2 - 4) equal to a variable A and solve for x. This method allows for determining which values of A correspond to valid x values, thus identifying the range. The domain has been established as |x| > 2, which is crucial for understanding the function's behavior. Graphing is not necessary if the algebraic manipulation is performed correctly. Ultimately, the range can be derived from the valid outputs of the function based on the solved values of A.
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Homework Statement



Find the range of the function [URL=http://imageshack.us/photo/my-images/225/msp205619ffihh51bgcch8h.gif/][PLAIN]http://img225.imageshack.us/img225/5896/msp205619ffihh51bgcch8h.gif[/URL][/PLAIN].



Homework Equations





The Attempt at a Solution



I tried to solve it but ended up with nothing. Without drawing a graph, how can i find its range? The only thing i can get is domain of f = |x| > 2 but i couldn't find the range. Can anyone help me? Thank you..
 
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Michael_Light said:

Homework Statement



Find the range of the function [URL=http://imageshack.us/photo/my-images/225/msp205619ffihh51bgcch8h.gif/][PLAIN]http://img225.imageshack.us/img225/5896/msp205619ffihh51bgcch8h.gif[/URL][/PLAIN].



Homework Equations





The Attempt at a Solution



I tried to solve it but ended up with nothing. Without drawing a graph, how can i find its range? The only thing i can get is domain of f = |x| > 2 but i couldn't find the range. Can anyone help me? Thank you..

Set 2x/sqrt(x^2 - 4) to A, and solve for x. Each value of A for which there is an x value is in the range of your function.
 

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