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Consider the functions and defined by 

 

f(x)=sqrt((x+1)/(x-1)) 

 

and

 

g(x)=(sqrt x+1)/(sqrt x-1)

 

explain why f and g are not the same function.

 

Thanks!

WhichWitchIsWhich  Nov 1, 2017
 #1
avatar+88826 
+1

The first function is defined on (-inf, -1] U (1, inf )

 

However.........the second function  is only defined for (1, inf )

 

Note  that if let x = -2, the first function is

 

sqrt   ( [-2 + 1 ] / [ -2 -1] )  =  sqrt ( -1 / -3 )  =  sqrt (1/3)

 

But....in the second function we have

 

sqrt  [ -2 + 1 ]  / sqrt [ -2  - 1 ]  =  sqrt [ -1] / sqrt [ -3]  and the numerator/denominator are both non-real

 

 

cool cool cool

CPhill  Nov 1, 2017

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