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The functions \(f\) and \(g\) are defined as follows:

 

\(f(x) = \sqrt{\dfrac{x+1}{x-1}}\quad\text{and}\quad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}\)


Explain why the functions \(f\) and \(g\) are not the same function.

 Mar 8, 2020
 #1
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For -1 < x < 1 the two functions result in the same magnitude but have opposite sign.  For example: f(-0.5) = 0.577i and g(-0.5) = -0.577i.

 

.

 Mar 8, 2020
edited by Alan  Mar 8, 2020

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