Function: Find the range of the funtion

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SUMMARY

The discussion focuses on finding the range of the function defined by the expression 2x/sqrt(x^2 - 4). Participants highlight that the domain is restricted to |x| > 2. To determine the range without graphing, one participant suggests setting the function equal to a variable A and solving for x, indicating that each value of A corresponding to a valid x will be part of the function's range.

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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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