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Domain and range

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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
+118470
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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   !!!!!

Feb 5, 2021
edited by CPhill  Feb 5, 2021
#2
+128
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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
+118470
0

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

CPhill  Feb 5, 2021