Question 1164405
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<pre>

These two functions,  f(x)  and  g(x),  have different domain;  

in other words, they are defined in different sets of real numbers.


The domain for function g(x)  is  { x |  x > 1 }.


The domain for function f(x)  is  the set of solutions to THIS inequality

    {{{(x+1)/(x-1)}}} > 0,   


which is the UNION of two sets

    { x < -1 } U { x > 1 },


where the numerator and denominator BOTH are negative OR BOTH are positive.



See this visual illustration, where I slightly changed function g(x) intently to make the difference visible.


    {{{graph( 400, 400, -5, 5, -5, 10,
          sqrt((x+1)/(x-1)), sqrt(x+1)/sqrt(x-1) + 0.2          
)}}}


    Plot  f(x) = {{{sqrt((x+1)/(x-1))}}} (red), g(x) = {{{sqrt(x+1)/sqrt(x-1)}}} (green)


    f(x)  has two branches, as you see (two red lines);  

    g(x)  has only one branch (only one green line).
</pre>


Answered, solved and explained.


Is everything clear to you in my solution ?



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