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

 

 

Help is appreciated!!!

 Feb 5, 2021
 #1
avatar+118470 
+2

f ( f(x) )    =             1                                         1

                     _______________    =     _________________    =

                     2  (  1/ (2x  -5) ) - 5                2/ (2x  - 5)  - 5 

 

 

    2x   - 5                              2x   - 5

______________   =         ________

[ 2 -  5(2x - 5)]                     27  -10x

 

 

The  denominator  cannot =  0 

 

27  -10 x  = 0

 

27  = 10x

 

x =  27  /10      is not in the  domain

 

CORRECTED   !!!!!

     

 

 

cool cool cool

 Feb 5, 2021
edited by CPhill  Feb 5, 2021
 #2
avatar+128 
0

nice, CPhill! but when you solved for f(f(x)), did you maybe forget the 1/ part of the function?

 

and did you maybe do 2x+5 instead of 2x-5? or maybe you just did some simplifying and i didn't follow that, sorry if that is what you did and i just didn't notice ;o

macar0ni  Feb 5, 2021
edited by macar0ni  Feb 5, 2021
edited by macar0ni  Feb 5, 2021
edited by macar0ni  Feb 5, 2021
edited by macar0ni  Feb 5, 2021
 #3
avatar+118470 
0

Oops...slight error....corrected  now  !!!

 

cool cool cool

CPhill  Feb 5, 2021

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