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0
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avatar+809 

Let \(f(x)=\frac{1}{2x-5}\). Find the largest \(x\) which is not in the domain of \(g(x)=f(f(x))\).

 Dec 24, 2018
 #1
avatar+98102 
+2

g(x) =  f ( f(x)  =

 

              1

_________________   =

 2   ( 1 / [2x - 5] ) - 5 

 

 

              1

_____________________   =

      2        -       5

______

  2x - 5

 

 

       2x  -   5

____________________    =

    2  -  5 [ 2x - 5]

 

 

      2x  - 5

____________

    27 - 10x

 

The x not in the domain  is

 

27 - 10x  = 0

 

27 = 10x

 

27 / 10  

 

 

 

cool cool cool

 Dec 25, 2018
edited by CPhill  Dec 25, 2018
 #2
avatar+809 
0

Thanks you, CPhill!

mathtoo  Dec 25, 2018
 #3
avatar+3994 
+3

I just read about pretty hard functions, hope I can solve it!!

\(g(x)=f(f(x))=\frac{1}{2x-5}=\frac{1}{2(\frac{1}{2x-5})-5}=\frac{2x-5}{27-10x}\)

Thus, the largest \(x\) not in the domain of \(g(x)\) is .\(\boxed{\frac{27}{10}}.\)

.
 Dec 25, 2018
 #4
avatar+98102 
0

Good job, tertre....!!!

 

cool cool cool

CPhill  Dec 26, 2018

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