+0  
 
0
46
4
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+94453 
+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+3729 
+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+94453 
0

Good job, tertre....!!!

 

cool cool cool

CPhill  Dec 26, 2018

25 Online Users

avatar
avatar
avatar

New Privacy Policy

We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive information about your use of our website.
For more information: our cookie policy and privacy policy.