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Let\(f(x)=\frac{1}{x-3} \) . Find the largest \(x\) that is not in the domain of \(g(x)=f(f(x))\).

 Mar 10, 2019
 #1
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f(f(x))  =          1                             1                                 x  -  3

               ___________   =       ____________   =       _________

                [1 / {x - 3)] -3               [ 1 - 3(x - 3)]                 10 - 3x

                                                  ___________

                                                      (x -  3)

 

 

The numerator has no effect on the domain

 

The domain will be all x's  except those where 10 - 3x = 0

 

So....the domain includes all x's   except  x = (10/3)

 

See the graph here : https://www.desmos.com/calculator/yovhfn2ymb

 

 

cool cool cool

 Mar 10, 2019

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