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Any help is appreciated! I tried finding the inverse but I don't know the next step. Can someone please help, thanks!! Let f(x)=3x-4 and g(x)=5x+c . Find c if f(g(x) and g(f(x) for all x. smiley

 Jan 13, 2024

Best Answer 

 #1
avatar+36923 
+1

Your question does not ask for the inverse of any of the functions....sooooo....

f(x) = 3x-4      then  for f (g(x) )  put   g(x) in place of 'x'

   f(g(x)) = 3 (5x+c) - 4    = 15x + 3c - 4 

 

and 

g(f(x)) = 5 (3x-4) +c  = 15x - 20 + c         

 

Now your question is missing something.....I will assume you want the two to be equal for all x 

   15x -20 + c = 15x + 3c - 4 

  -20 + c = 3c -4 

    -16 = 2c 

         c = - 8           

 Jan 13, 2024
edited by ElectricPavlov  Jan 13, 2024
 #1
avatar+36923 
+1
Best Answer

Your question does not ask for the inverse of any of the functions....sooooo....

f(x) = 3x-4      then  for f (g(x) )  put   g(x) in place of 'x'

   f(g(x)) = 3 (5x+c) - 4    = 15x + 3c - 4 

 

and 

g(f(x)) = 5 (3x-4) +c  = 15x - 20 + c         

 

Now your question is missing something.....I will assume you want the two to be equal for all x 

   15x -20 + c = 15x + 3c - 4 

  -20 + c = 3c -4 

    -16 = 2c 

         c = - 8           

ElectricPavlov Jan 13, 2024
edited by ElectricPavlov  Jan 13, 2024
 #2
avatar+19 
+1

Yes, your assumption was right, im sorry for the confusion! Thanks for your help.

breadysetgo  Jan 13, 2024

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