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if f(g(x))=x and f(x)= 3x-4, find g(x)

Mathematics
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  • hba
to find the inverse function, let y=g(x) f(y)=x 3y-4= x rearrange to find y and voila ! you get g(x)
  • hba
Notice that \[f(g(x))=x=f(f^{-1}(x))\] thus \[g(x) = f^{-1}(x)\]
  • hba
@stevench got it ?

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Other answers:

i got it, but dont know how to re arrange it to where it fits in the options im given
  • hba
What did you get ? and What are your options ?
a) x-4/3 b) x+4/3 c) (x/3) +4 d) (x/3) -4
  • hba
What answer did you get ? @stevench
  • hba
@stevench Reply ?
  • hba
What answer did you get ?
I'm trying to do a billion things at once becaus I'm way overdue in an online class and just need help gettin answers
  • hba
You dont know how to solve 3y-4=x
  • hba
Just rearrange to find y
  • hba
@ikhwanz Please read the CoC-http://openstudy.com/code-of-conduct
  • hba
Before you answer.
easily you arrange it \[(f^-1(f(g(x))\] put the value of f(g(x)) inside f^-1 f-1=(x+4)/3_________ which from f(x)=3x-4 so change y=3x-4 then get the x value y+4/3 change f(y) to f-1=(x+4)/3 subtitute value fg(x) inside f-1
  • hba
@stevench You should also look at the CoC.
Thank you @ikhwanz for helping me find the answer
As a rule of thumb, we would prefer the askers to participate in the solution process instead of having the answerers doing all the work. if f(g(x))=x and f(x)= 3x-4, find g(x) f(x)= 3x-4; replace x with a g(x) to get f(g(x))= 3[g(x)] - 4 ; and since f(g(x))=x x = 3[g(x)] - 4 , use basic algebra techniques to find g(x)
well at the moment in everything that i am trying to do I can't just simply wait all day
thats not really our concern; we are aimed at being a study site, not a free answering service. We would rather promote learning the material as opposed to just handing over answers. This social contract is aimed at curbing people from using the site to cheat with ...

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