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# Inverse Functions!

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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.

Jan 13, 2024

#1
+36923
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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
+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

ElectricPavlov Jan 13, 2024
edited by ElectricPavlov  Jan 13, 2024
#2
+19
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Yes, your assumption was right, im sorry for the confusion! Thanks for your help.