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If \(f(x)=g(g(x))-g(x)\) and \(g(x)=2x-1\), find \(f(3).\).

 Aug 27, 2018
 #1
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+1

The answer is 4

g(g(x))=9

g(x)=5

9-5=4

 Aug 27, 2018
 #2
avatar+7612 
+1

f(x)  =  g(g(x)) - g(x)        Plug in  3  for  x .

f(3)  =  g(g(3)) - g(3)

 

g(x)  =  2x - 1         Now let's find  g(3) .  Plug in  3  for  x .

g(3)  =  2(3) - 1

g(3)  =  6 - 1

g(3)  =  5

 

f(3)  =  g(g(3)) - g(3)       Substitute  5  in for  g(3) .

f(3)  =  g(5) - 5

 

g(x)  =  2x - 1        Now let's find  g(5) .  Plug in  5  for  x .

g(5)  =  2(5) - 1

g(5)  =  10 - 1

g(5)  =  9

 

f(3)  =  g(5) - 5                Substitute  9  in for  g(5) .

f(3)  =  9 - 5

f(3)  =  4

 Aug 27, 2018

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