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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 5, 2020
edited by Guest  Mar 5, 2020
 #1
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\(f(x) = \sqrt{\dfrac{x+1}{x-1}}\quad\text{and}\quad g(x) = \dfrac{\sqrt{x+1}}{\sqrt{x-1}}\)

 

Note  that   f(x)  will  be defined  whenever   x  ≤  - 1     and  x > 1

 

But  note  that  g(x)  is  only  defined  whenever  x  > 1......

 

See the graph here to get a feel for this  :

 

https://www.desmos.com/calculator/lhfhhtc98o

 

 

cool cool cool

 Mar 5, 2020

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